LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNI 


Class 


EXERCISES  IN  SURVEYING 

FOR 

FIELD  WORK  AND  OFFICE  WORK 

WITH 

QUESTIONS  FOR  DISCUSSION 

INTENDED  FOR   USE  IN   CONNECTION  WITH    THE 
AUTHOR'S  BOOK 

PLANE  SURVEYING 


BY 

JOHN  CLAYTON  TRACY,  C.E. 

ASSISTANT  PROFESSOR  OF  STRUCTURAL  ENGINEERING 

SHEFFIELD  SCIENTIFIC  SCHOOL  OF 

YALE  UNIV-EBSITV 


FIRST  EDITION 

FIRST    THOUSAND 


NEW  YORK 
JOHN  WILEY  &  SONS 

LONDON:    CHAPMAN   &   HALL,  LIMITED 
1909 


•  O 


COPYRIGHT,  1908,   1909, 

BY 

JOHN  CLAYTON  TRACY 


Stanbopc  ipresa 

F.  H.  GILSON  COMPANY 
BOSTON.  U.S.A. 


PREFACE. 


THIS  book  of  exercises  is  intended  for  use  in  connection  with 
the  author's  book  on  ''Plane  Surveying."  Part  I  consists  of 
exercises  in  field  work  grouped  according  to  the  nature  of  the 
work.  Part  II  consists  of  exercises  in  office  computations  and 
in  plotting.  (See  page  110.)  The  whole  constitutes  a  thorough 
introductory  course  in  fundamental  principles  and  methods.  So 
far  as  the  author  is  aware,  this  is  the  first  attempt  to  offer  a 
collection  of  problems  in  both  field  work  and  office  work,  and 
the  first  book  of  exercises  to  be  published  for  use  in  connection 
with  a  text-book. 

The  author  is  convinced  from  his  own  experience  that  the  most 
effective  course  in  field  work  is  not  that  in  which  the  chief  aim 
is  to  make  a  complete  survey  of  a  more  or  less  extensive  territory. 
On  the  contrary,  much  time  may  be  lost  in  undertaking  work  for 
which  the  student  is  not  prepared,  and  still  more  may  be  wasted 
in  requiring  the  student  to  repeat  the  same  kind  of  work  day 
after  day  merely  to  cover  a  given  amount  of  territory.  It  is  far 
better  to  begin  with  a  systematic  course  of  exercises  which  shall 
serve  not  only  as  a  preliminary  drill  in  the  use  of  instruments, 
but  also  as  a  careful  study  of  the  various  methods  which  underlie 
all  surveying.  Not  only  will  the  student  be  better  prepared  for 
subsequent  courses  in  municipal,  mining,  railway  and  geodetic 
surveying,  but  the  effect  of  such  a  thorough  introductory  course 
will  be  felt  after  graduation  in  whatever  kind  of  surveying  he 
may  be  engaged.  For  this  reason  such  a  course  may  well  extend 
over  the  first  two  college  years. 

A  feature  of  this  book  will  be  found  in  the  questions  suggested 
for  discussion  at  the  end  of  nearly  every  exercise.  Some  years 
ago  the  author  adopted  the  practice  of  holding  quizzes  in  the  field 
in  connection  with  each  new  piece  of  work.  For  example,  an 
instructor  has  charge  of  a  small  squad  of  men  to  whom  problems 
in  chaining  have  been  assigned.  As  soon  as  the  work  is  finished, 
he  gathers  his  men  about  him,  and  questions  them  on  various 
matters  pertaining  to  chaining,  such,  for  example,  as  the  use  of 
the  steel  tape,  the  sources  of  error,  different  methods  of  doing  the 
work  just  completed  and  the  advantages  and  disadvantages  of 

iii 

187737 


IV  PREFACE. 

these  methods.  In  some  other  part  of  the  field  another  instructor 
may  be  holding  a  similar  quiz  on  leveling  or  on  transit  work. 
These  quizzes,  if  properly  conducted;  often  develop  into  interest- 
ing discussions  in  which  many  important  points  are  brought  out 
that  would  entirely  escape  the  student  if  he  were  merely  required 
to  do  the  field  work  assigned.  Moreover,  the  student  may  be 
expected  to  take  his  text-book  into  the  field  with  him,  and  to 
spend  such  spare  time  as  he  may  have  in  looking  up  answers  to 
questions  which  he  knows  will  be  asked  at  the  end  of  the  exercise. 
A.  great  deal  of  the  recitation  work  usually  held  in  the  class-room 
will  be  much  more  effective  if  it  is  transferred  to  the  field  in  this 
way.  If,  however,  it  is  found  inexpedient  to  hold  these  quizzes 
and  discussions  hi  the  field,  the  questions  may  still  be  used  by  the 
earnest  student  to  develop  his  knowledge  of  the  subject.  They 
should  prove  particularly  valuable  to  young  men  in  practice  who 
are  seeking  to  perfect  themselves  in  the  art  of  surveying. 

In  most  courses  it  probably  will  be  found  necessary  to  omit 
some  of  the  exercises  given  in  this  book.  It  is  suggested,  how- 
ever, that  the  student  be  held  responsible  for  answers  to  the 
questions  in  the  omitted  exercises,  and  that,  if  possible,  these 
questions  be  made  a  basis  for  class-room  discussion. 

Unless  otherwise  stated,  all  paragraph  and  page  references  are 
to  the  author's  text-book  and  not  to  this  book. 

JOHN  C.  TRACY. 
NEW  HAVEN,  CONNECTICUT. 
June,  1909. 


INDEX   OF  GROUPS. 


PART  I.  — FIELD  WORK. 

GROUP  PAGES 

E.       Introductory  Exercises  (For  the  Classroom.) 1-5 

C.        Exercises  in  Chaining 6-17 

T.        Exercises  in  the  Use  of  the  Transit 18-28 

Tr.      Exercises  in  Running  Transit  Lines 29-37 

Ts.      Transit  Surveys 38-41 

Tp.     Special  Problems  in  Transit  Surveying 42-50 

L.        Exercises  in  Leveling 51-62 

Ls.      Special  Problems  in  Leveling 63—68 

Co.      Exercises  in  the  Use  of  the  Compass 69-72 

S.        Exercises  in  the  Use  of  the  Stadia 73-78 

P.        Exercises  in  the  Use  of  the  Plane  Table 79-83 

To.     Exercises  in  Topographic  Surveying 84-88 

M.       Exercises  in  Determining  a  True  Meridian 89-94 

I.        A  Study  of  Surveying  Instruments 95-101 

A.       Adjustments 102-109 


PART  II.  —  OFFICE  WORK. 

G.       General  Methods  of  Computation 111-115 

B.       Calculation  of  Bearings 116-120 

L.        Latitudes  and  Departures 121-124 

T.        Triangulation 125-127 

O.       Omitted  Measurements 128-136 

A.       Areas 137-143 

E.       Earthwork  Calculation 144-150 

P.        Exercises  in  Plotting 151-160 

Q.       Questions  Pertaining  to  Mapping 161-168 


TABLE   OF   CONTENTS. 


PART  I.  —  FIELD  WORK. 

GROUP  E. 

Introductory  Exercises. 

(For  the  Classroom.) 

EXERCISK  PAGE 

E-l.     Definitions,   Fundamental  Principles   and   General 

Methods 1 

E— 2.     General  Discussion  of  Errors 3 

E— 3.     General  Discussion  of  Field  Notes 5 

E-4.     Single  Stroke  Lettering 5 


GROUP  C. 

Exercises  in  Chaining. 

(XL     Reading  a  Chain  Tape 6 

C-2.     Chaining  Distances  Greater  than  the  Length  of  the 

Tape 7 

C-3.     Chaining  on  a  Slope 8 

C-4.     Standardizing  the  Tape 8 

C-5.     Experiments  with  a  Steel  Tape 9 

C— 6.     Measuring  a  Base  Line 10 

C-7.     A  Chain  Survey  of  an  Irregular  Polygon 11 

C-8.     To  Chain  from  a  Given  Point  over  the  Brow  of  a 

Hill  to  Another  Point 11 

C-9.     Laying  Out  a  Right  Angle  with  a  Tape   by  the 

3-4-5  Method 12 

C-10.     To    Erect   a   Perpendicular   with   a   Tape   at   Any 

Point  in  a  Line 12 

C-ll.     To  Run  One  Line  Parallel  to  Another  Line 13 

C-12.     To  Measure  between  Two  Points  When  a  Corner  of  a 

Building  Intervenes 13 

C-13.     To  Measure  to  an  Inaccessible  Point 13 

C-14.     To  Measure  the  Angles  of  a  Triangle  with  a  Tape  . .  14 
C-15.     A  Chain  Survey  of  a  Plot  of  Ground  with  Irregular 

Boundary  Lines  and  Containing  Buildings 15 

C— 16.     Discussion  of  Errors  in  Linear  Measurements 16 

vii 


Vlll 


TABLE    OF    CONTENTS. 


GROUP  T. 

Exercises  in  the  use  of  the  Transit. 

EXERCISE  PAGE 

T-l.     Setting  up  a  Transit 18 

T-2.     Prolonging  a  Straight  Line , 19 

T-3.     Balancing  in  a  Transit 20 

T-4.     Reading  the  Limb  of  a  Transit 20 

T-5.     Reading  Angles  (Limb  and  Vernier) 22 

T-6.     Measuring  Horizontal  Angles  with  a  Transit 23 

T-7.     Practice  in  Doubling  Horizontal  Angles 24 

T-8.     Measuring  Vertical  Angles  with  a  Transit 24 

T-9.     To  Find  the  Intersection  of  Two  Lines  of  Sight 25 

T-10.     To  Establish  a  Line  of  Sight  Parallel  to  a  Fence 

or  to  a  Building 26 

T-ll.     To  Measure  an  Angle  Formed  by  Two  Intersecting 

Lines  Without  Setting  up  over  Either  Line 26 

T-l  2.     Discussion  of  the  Errors  in  Angular  Measurement . .  27 


GROUP  Tr. 

Exercises  in  Running  Transit  Lines. 

Tr-1.     Survey  of  a  Triangle  or  Polygon   by   the   Direct 

Angle  Method 30 

Tr-2.  Measuring  the  Exterior  Angles  of  a  Triangle  or 

Polygon 31 

Tr-3.  Doubling  the  Interior  Angles  of  a  Triangle  or 

Polygon 31 

Tr-4.  Doubling  the  Exterior  Angles  of  a  Triangle  or 

Polygon 31 

Tr— 5.  Measuring  the  Interior  Angles  of  a  Triangle  or 

Polygon,  and  Checking  by  Calculated  Bearings .  .  32 
Tr-6.  Measuring  the  Interior  Angles  of  a  Triangle  or 

Polygon  to  the  Left 33 

Tr-7.  Measuring  the  Exterior  Angles  of  a  Triangle  or 

Polygon  to  the  Left 33 

Tr— 8.  Measuring  the  Deflection  Angles  of  a  Triangle  or 

Polygon 34 

Tr-9.  Survey  of  a  Triangle  or  Polygon  by  the  First 

Azimuth  Method 34 

Tr— 10.  Survey  of  a  Triangle  or  Polygon  by  the  Second 

Azimuth  Method 36 

Tr-11.  Survey  of  a  Triangle  or  Polygon  by  the  Method  of 

Bearings 36 

Tr-1 2.  Questions  on  the  Methods  of  Running  Transit  Lines 

or  Traverses .  .  37 


TABLE    OF   CONTENTS. 


GROUP  Ts. 

Transit  Surveys. 

EXERCISE  PAGE 

Ts-1.     Discussion  of  the  Methods  of  Locating  Details 38 

Ts-2.     Discussion  of  the  Methods  of  Keeping  Field  Notes.  39 
Ts-3.     Discussion  of  Practical  Questions  of  Field  Work  in 

Transit  Surveying 40 

Ts-4.     Transit  Survey  of  a  Small  Area 41 


GROUP  Tp. 

Special  Problems  in  Transit  Surveying. 

Tp— 1 .  Practice  in  Triangulation 42 

Tp-2.  'To  Prolong  a  Straight  Line  through  an  Obstacle ...  43 
Tp-3.  To  Run  a  Line  between  Two  Given  Points  When 

an  Obstacle  Intervenes 44 

Tp-4.  To  Measure  between  Two  Points  When  One  is 

Inaccessible 44 

Tp-5.  To  Measure  between  Two  Points  When  Both  are 

Inaccessible 45 

Tp-6.  To  Measure  the  Height  of  an  Inaccessible  Point. ...  45 

Tp-7.  Perpendiculars  and  Parallels 46 

Tp-8.  To  Stake  Out  a  Building 46 

Tp-9.  To  Locate  Piers  for  a  Bridge 48 

Tp-10.  To  Stake  Out  a  Circle  with  a  Transit  and  a  Tape . .  49 


GROUP  L. 

Exercises  in  Leveling. 

L-l .     Setting  up  the  Level 51 

L-2.     Reading  the  Leveling  Rod 52 

L-3.     To  Find  the  Probable  Error  of  Sighting  and  of  Set- 
ting a  Target 53 

L— 4.     Comparison  of  Readings  Taken  With  and  Without 

the  Target 54 

L-5.     To  Test  the  Sensitiveness  of  a  Level  Bubble 54 

L-6.     Differential  Leveling 55 

(A  Study  of  the  Theory.) 

L-7.     Differential  Leveling 56 

(A  Study  of  Field  Methods.) 

L-8.     Profile  Leveling 58 

L— 9.     Discussion  of  Errors  in  Leveling 58 

L-10.     Use  of  the  Hand  Level 60 

L— 11.     Trigonometric  Leveling 60 

L— 12.     Barometric  Leveling 62 


TABLE   OF   CONTENTS. 


GROUP    Lp. 

Special  Problems  in  Leveling. 

EXERCISE   .  PACK 

Lp-1.  Reciprocal  Leveling 63 

Lp-2.  To  Set  Stakes  on  a  Grade  Between  Two  Fixed 

Points  (Special  Method} 63 

Lp-3.  To  Set  Grade  Stakes  between  Two  Fixed  Points 

When  the  Ground  is  Uneven 65 

Lp-4.  Use  of  the  Gradienter 66 

Lp-5.  To  Estimate  Cut  and  Fill  for  Grading 66 

Lp-6.  To  Stake  Out  a  Vertical  Curve 67 


GROUP    Co. 

Exercises  in  the  Use  of  the  Compass. 

Co— 1.     The  Error  of  Sighting  and  Reading  a  Compass  ....        69 

Co-2.     Reading  Bearings 70 

Co-3.     Compass  Survey  of  a  Polygon 71 

GROUP    S. 
Exercises  in  the  Use  of  the  Stadia. 

S-l.     To  Test  the  Stadia  Interval 73 

S-2.     To    Measure    Distances  on    Level  Ground    by  the 

Stadia 74 

S— 3.     To     Measure     Horizontal     Distances     on     Sloping 

Ground  by  the  Stadia 75 

S— 4.     To  Obtain  Vertical  Distances  or  Elevations  by  the 

Stadia 75 

'  S-5.     Stadia  Survey  of  a  Polygon 77 

(Azimuth  Method.) 

GROUP    P. 

Exercises  in  the  Use  of  the  Plane  Table. 

P-l.     Plane-table  Survey  of  a  Polygon 79 

(Method  of  Radiation.) 
P-2.     Plane-table  Survey  of  a  Polygon 80 

(Method  of  Progression,  or  Traversing.) 

P-3.     Plane-table  Survey  of  a  Polygon 80 

(Method  of  Radio-Progression.) 

P-4.     Plane-table  Survey  of  a  Polygon 81 

(Method  of  Intersection.) 

P-5.     Plane-table  Survey  of  a  Polygon 81 

(Method  of  Resection.) 

P-6.     Discussion  of  Plane-table  Surveying 81 

P-7.     Plane-table  Practice  in  the  Three-point  Problem  ...  82 


TABLE   OF   CONTENTS.  XI 

GROUP    To. 
Exercises  in  Topographic  Surveying. 

XERCISE  PAGE 

To-1 .     Running  in  a  Contour 84 

To-2.     Topographic  Survey  of  a  Small  Area ' 85 

(Direct  Method  of  Running  in  Contours  with  a  Spirit 
Level.) 

To-3.     Topographic  Survey  of  a  Small  Area F 6 

(Contours  Interpolated  by  Spirit  Leveling.) 

To-4.     Topographic  Survey  of  a  Small  Area 86 

(Contours  Interpolated  by  the  Vertical-Angle  Method.) 
To-5.     Questions  Pertaining  to  Topographic  Surveying 87 

GROUP    M. 

Exercises  in  Determining  a  True  Meridian. 

M— 1.  Determination  of  a  Meridian  by  Observations  on 

Polaris  at  Elongation 89 

M-2.  Determination  of  a  Meridian  by  a  Single  Observation 

on  the  Sun 91 

M-3.  Determination  of  a  Meridian  with  a  Solar  Attach- 
ment    93 

GROUP    I. 

A  Study  of  Surveying  Instruments. 

1-1.  The  Vernier,   the  Magnetic   Needle  and  the  Level 

Bubble : 95 

1-2.     Theory  of  Lenses 96 

1-3.     The  Telescope 97 

1-4.     Chains  and  Tapes 98 

1-5.     The  Transit 98 

1-6.     The  Level 99 

1-7.     Leveling  Rods  and  Stadia  Rods 99 

1-8.     The  Compass,  the  Plane  Table  and  the  Sextant 100 

1-9.     The  Care  of  Instruments 100 

GROUP    A. 

Adjustments. 

A-l.  Preliminary  Discussion  of  Adjustments 102 

A-2.  Adjustments  of  the  Transit 103 

A-3.  Adjustments  of  the  Wye-Level 105 

A-4.  Adjustments  of  the  Dumpy  Level 107 

A-5.  Adjustments  of  the  Compass 108 

A-6.  Adjustments  of  the  Plane  Table 108 

A-7.  Adjustments  of  the  Sextant 109 


TABLE    OF   CONTENTS. 


PART  II. —OFFICE  WORK. 


GROUP    G. 

General  Methods  of  Computation. 

EXERCISE  PAGE 

G-l .     Short  Cuts  in  Arithmetical  Work Ill 

G-2.     Consistent  Accuracy  in  Computations 112 

G-3.     Trigonometric   Relations   Between   the  Sides  of  a 

Right-Angled  Triangle 113 

G-4.     Use  of  Logarithms 114 


GROUP    B. 

Calculation  of  Bearings. 

B-l.     Calculation  of  Bearings  from  Angles 116 

B-2.     Changing  the  Bearings  of  All  Lines  of  a  Traverse 

by  a  Given  Amount 118 

B-3.     Calculation  of  Angles  from  Bearings   118 

GROUP    L. 

Latitudes  and  Departures. 

L.     Calculation  of  Latitudes  and  Departures    121 

GROUP    T. 

Triangulation. 

T— 1.     Computations  for  Triangulations 125 

T-2.     Miscellaneous  Problems  in  Triangulation 127 

GROUP    O. 

Omitted  Measurements. 

O-l.     To  Calculate  the  Bearing  and  Length  of  an  Omitted 

Side  of  a  Polygon 128 

O-2.  To  Calculate  the  Omitted  Bearing  of  One  Side  and 

the  Omitted  Length  of  Another  Side  of  a  Polygon .  129 
O-3.  To  Calculate  the  Omitted  Lengths  of  Two  Sides  of 

a  Polygon 131 

O-4.  To  Calculate  the  Omitted  Bearings  of  Two  Sides 

of  a  Polygon 133 

O-5.  Calculation  of  Omitted  Measurements 134 

(Miscellaneous  Problems  ) 


TABLE  OF   CONTENTS.  xiii 


GROUP    A. 

Areas. 

EXERCISE     '  PAGE 

A-l .     The  Use  of  the  Planimeter 137 

A-2.     To  Compute  Areas  Directly  from  Field  Measure- 
ments       137 

A-3.     Calculation  of  Areas  from  Offsets 138 

A— 4.     Calculation   of  Areas  from  Latitudes  and  Double 

Longitudes 139 

A-5.     To  Part  Off  a  Required  Area  by  a  Line  Having  a 

Given  Direction 141 

A-6.     To  Part  Off  a  Required  Area  by  a  Line  Starting 

from  a  Given  Point 142 


GROUP    E. 

Earthwork  Calculation. 

E-l.     To  Calculate   Earthwork  by  the  Method  of  Unit 

Areas 144 

(All  Cut  or  all  MIL) 

E-2.     To  Calculate   Earthwork  by  the  Method  of  Unit 

Areas 146 

(Irregular  Boundaries.) 

E-3.     To  Estimate  Cut  and  Fill  by  the  Method  of  Unit 

Areas 147 

E-4.     To  Calculate  Cut  and  Fill  by  the  Method  of  Unit 

Areas 148 

(Irregular  Boundaries.) 

E-5.     Calculation  of  Earthwork  for  Ditches  and  Embank- 
ments        149 

E-6.     To  Estimate  Cut  and  Fill  from  a  Contour  Map ....      150 


GROUP    P. 

Exercises  in  Plotting. 

P-l.     Use  of  Drawing  Instruments 151 

P-2.     Methods  of  Plotting  Angles 153 

P-3.     Plotting  Traverses  with  a  Protractor 155 

P-4.     Tangent  Method  of  Plotting  Traverses 156 

P-5.     Chord  Method  of  Plotting  Traverses 156 

P-6.     Plotting  Traverses  by  Bearings 157 

(Tangent  Method.) 

P-7.     Plotting  Traverses  by  Bearings 158 

(Chord  Method.) 

P-8.     Plotting  Traverses  by  Azimuths 158 

P-9.     Plotting  Traverses  by  Latitudes  and  Departures  ...  159 

P-10.     Plotting  the  Survey  on  Page  184 160 


TABLE   OF    CONTENTS. 


GROUP    Q. 

Questions  Pertaining  to  Mapping. 

EXERCISE  PAGE 

Q-l.     Working  up  Field  Notes  Preparatory  to  Plotting.  .  .  161 

Q-2.     Plotting  the  Map 162 

Q-3.     Plotting  Traverses 163 

Q-4.     Plotting  Details 164 

Q-5.     Finishing  the  Map 165 

Q-6.     Profiles 168 


OF  THE 

/    UNIVERSITY  } 

OF 


Exercises  in  Plane  Surveying, 


PART  I. 

FIELD  WORK. 


GROUP  E. 

INTRODUCTORY  EXERCISES. 

This  group  of  exercises,  consisting  principally  of  questions  for  class-room 
discussion,  are  intended  to  cover  those  fundamental  principles  and  methods 
which  the  student  should  know  before  beginning  field  work.  The  exercise 
on  single-stroke  lettering  is  inserted  for  the  benefit  of  students  who  have  not 
had  a  systematic  course  in  freehand  lettering. 

Exercise  E-l. 

Definitions,  Fundamental  Principles  and  General 
Methods. 

Reference:  Chapter  I,  pp.  1-8. 

Questions:  1.  What  is  meant  in  geodesy  by  the  earth's  sur- 
face? p.  1.  2.  When  is  it  necessary  to  make  this  distinction 
in  ordinary  surveying?  3.  What  is  the  shape  of  the  earth's 
surface?  4.  What  is  the  average  radius?  5.  What  is  the 
difference  in  lengths  between  the  long  and  short  axes,  expressed 
in  miles?  6.  What  is  meant  by  sea-level,  and  how  can  it  be 
determined  at  any  given  place?  7.  Define  horizontal  plane; 
vertical  plane.  8.  What  is  the  difference  between  a  horizontal 
plane  and  a  level  surface?  9.  What  is  the  significance  of  the 
two  terms  "plane"  and  "geodetic"  as  applied  to  surveying? 
p.  2.  10.  What  is  the  approximate  curvature  of  the  earth's 
surface  per  mile?  11.  How  large  an  area  may  be  covered  by 
the  methods  of  plane  surveying  without  involving  appreciable 
errors?  12.  Give  the  approximate  difference  in  length  between 
the  arc  on  the  earth's  surface  and  a  straight  line.  13.  What 
four  kinds  of  measurements  are  made  in  plane  surveying? 
(Illustrate  by  means  of  a  sketch.)  14.  If  a  farm  is  on  a  side 

1 


2  INTRODUCTORY  EXERCISES. 

hill,  would  a  map  of  that  farm  show  the  actual  area  of  the  surface? 
15.  What  are  the  units  of  linear  measurement  used  in  surveying 
in  the  United  States?  p.  3.  16.  What  are  the  units  of  angular 
measurement?  17.  In  making  certain  kinds  of  surveys,  as 
for  example,  a  survey  for  an  architect,  is  it  ever  customary  for 
the  surveyor  to  measure  in  feet  and  inches?  18.  What  is  a 
convenient  method  of  converting  hundredths  of  a  foot  to  fractions 
of  an  inch?  19.  From  the  table  on  page  650,  change  6  feet 
4|  inches  to  feet  and  decimals  of  a  foot.  20.  What  is  the 
standard  yard?  p.  3.  21.  In  this  country  where  may  a  steel 
tape  be  sent  to  be  compared  with  a  standard  length?  p.  561. 
21.  What  is  the  equivalent  of  one  metre  in  feet?  p.  3.  22.  What 
is  the  equivalent  of  one  vara  in  inches?  23.  What  other  units 
of  measurements  are  sometimes  used?  24.  Why  was  66  feet 
adopted  as  the  length  of  Gunter's  chain?  25.  How  would  you 
record  eight  chains,  six  links?  p.  33,  §  49.  26.  Reduce  sixty 
links  to  feet?  27.  Explain  the  method  of  locating  a  given 
point  with  reference  to  two  other  points  by  linear  measurements 
only.  p.  4.  28.  Explain  two  methods  of  locating  a  point  by 
angle  and  distance.  29.  Explain  the  method  of  locating  a 
point  by  angles  only.  30.  Explain  two  other  methods  of 
locating  a  point.  31.  Into  what  three  parts  may  the  work  of  a 
surveyor  be  divided?  p.  5.  32.  Of  what  does  the  field  work 
consist?  33.  Of  what  does  the  office  work  consist?  34.  Name 
some  of  the  important  questions  in  surveying  which  arise  in 
connection  with  field  work.  p.  6.  35.  Explain  by  different 
illustrations  how  the  purpose  of  a  survey  helps  to  decide  some 
of  these  questions.  36.  What  can  you  say  regarding  limits 
of  error  and  consistent  accuracy?  p.  7.  37.  Upon  what  does 
speed  depend?  p.  8.  38.  How  does  system  in  surveying  diminish 
the  chances  of  error? 


INTRODUCTORY    EXERCISES.  O 

Exercise  E-2. 
General  Discussion  of  Errors. 

Reference:  Chapter  II,  pages  9  to  19. 

Questions:  1.  What  is  the  true  error  of  any  measurement?  p.  9. 
2.  Why  is  the  true  error  never  known?  3.  In  general,  what  are 
the  three  sources  of  error?  4.  What  are  the  three  classes  of 
error?  5.  Explain  carefully  the  difference  between  constant 
errors  and  accidental  errors,  p.  10.  6.  Can  the  constant  error 
involved  in  any  measurement  be  reduced  by  repeating  the 
measurement  a  number  of  times  and  taking  the  mean  of  all  the 
measurements?  7.  What  is  the  object  in  repeating  the  measure- 
ments and  taking  the  mean?  8.  Give  a  few  illustrations  of 
what  is  meant  by  mistakes;  accidental  errors;  constant  errors? 
9.  Why  may  variations  in  sources  of  constant  error  be  classed 
as  accidental  errors?  p.  11.  10.  How  may  constant  errors  from 
different  sources  tend  to  balance  each  other?  11.  How  may 
constant  errors  from  the  same  source  tend  to  balance  each 
other?  12.  Explain  the  difference  between  cumulative  and 
compensating  errors.  13.  Explain  the  difference  between 
discrepancy  and  error.  14.  How  can  the  discrepancy  between 
two  measurements  be  small  yet  the  error  large?  p.  12.  15.  What 
can  you  say  as  regards  the  elimination  of  constant  errors? 
16.  How  may  mistakes  be  eliminated?  17.  Illustrate  how 
constant  errors  may  be  eliminated.  18.  How  may  accidental 
errors  be  reduced?  p.  13.  19.  What  can  you  say  as  regards  the 
relative  importance  of  errors  from  different  sources?  20.  What 
is  meant  by  an  appreciable  error?  21.  What  is  the  most 
probable  value  of  a  quantity,  when  several  measurements  have 
been  made  of  that  quantity?  22.  When  the  sum  of  several 
measurements  should  equal  the  exact  quantity,  how  is  the  true 
error  distributed?  p.  14.  23.  If  the  true  error  of  a  measurement 
is  never  known,  how  can  the  error  of  1'  or  60",  in  the  illustration 
on  page  14,  Case  1,  be  called  a  true  error?  24.  Explain  by 
illustration  how  the  discrepancy  should  be  distributed,  when 
the  sum  of  several  measurements  should  equal  some  other 
measurement.  25.  Why,  in  Case  2,  p.  14,  is  the  term  "discrep- 
ancy" used  instead  of  "error"? 

Questions  on  the  Method  of  Least  Squares:  26.  What  use  is 
made  of  the  method  of  least  squares?  p.  15.  27.  Upon  what 


4  INTRODUCTORY    EXERCISES. 

assumption  is  this  method  based?  28.  How  do  the  conditions 
in  practice  differ  from  those  of  the  assumption?  29.  What 
effect  has  this  on  a  most  probable  value  of  a  quantity  as  deter- 
mined by  the  method  of  least  squares,  and  how  may  the  prob- 
able value  be  made  to  approach  the  true  value?  30.  Define 
residual;  probable  error.  31.  In  surveying,  what  use  is  made 
of  most  probable  values;  probable  errors?  32.  Illustrate  how 
by  comparing  the  probable  errors  of  the  means  of  two  sets  of 
observations,  the  precision  of  one  mean  may  be  compared  with 
that  of  the  other,  p.  16.  33.  Explain  the  use  made  of  the  prob- 
able error  of  a  single  observation.  34.  How  can  the  weights 
which  should  be  given  to  different  sets  of  observations  be  found 
from  the  probable  errors?  35.  Upon  what  three  assumptions 
are  the  formulas  for  calculating  probable  errors  based?  p.  17. 
36.  What  additional  point  should  be  kept  in  mind?  37.  In 
order  that  probable  errors  may  be  of  any  significance,  what 
precautions  must  be  taken?  (See  Remark,  p.  17.)  38.  Two 
chainmen  measure  a  line  six  times  with  the  following  results 
in  feet:  314.124,  314.130,  314.133,  314.128,  314.136,  and  314.131. 
Two  other  chainmen  measure  the  same  line  with  the  following 
results  in  feet:  314.134,  314.124,  314.138,  314.122,  314.131,  and 
314.122.  What  is  the  relative  precision  of  the  work  of  the 
two  pairs  of  chainmen?  (See  illustration,  p.  19.)  39.  An 
angle  is  measured  with  a  transit  eight  different  times.  The 
degrees  and  minutes  being  the  same  but  the  seconds  varying  as 
follows:  20",  40",  30",  10",  20",  50",  30",  and  40".  The  same 
angle  was  measured  with  another  transit  with  the  following 
result:  40",  20",  20",  30",  40",  30",  30",  and  40".  Other  things 
being  equal,  which  is  the  better  instrument?  What  degree  of 
precision  may  be  expected  for  each  instrument  in  measuring  a 
given  angle  under  conditions  similar  to  those  prevailing  when 
the  above  angles  were  measured? 


INTRODUCTORY  EXERCISES.  5 

Exercise  E-3. 
General  Discussion  of  Field  Notes. 

Reference:  Chapter  III,  pages  20  to  30. 

Questions:  1.  What  are  field  notes?  2.  What  can  you  say 
as  regards  methods  of  keeping  notes?  3.  Give  general  sugges- 
tions for  keeping  notes,  p.  21.  4.  Into  what  three  parts  may 
field  notes  be  divided?  5.  Give  general  suggestion  for  record- 
ing numerical  values,  p.  22.  6.  Give  general  suggestions  for 
making  sketches,  p.  23.  7.  Give  general  suggestions  concerning 
explanatory  notes.  8.  What  style  of  lettering  should  be  used? 
p.  24.  9.  What  is  a  good  height  for  letters?  p.  29.  10.  How 
should  the  letters  be  spaced?  11.  Give  additional  suggestions 
for  taking  notes,  p.  29.  12.  Discuss  special  directions  for  class 
work.  p.  30. 

Exercise  E-4. 
Single  Stroke  Lettering. 

Reference:  Article  38,  pages  24  to  30. 

Directions:  In  this  exercise  use  a  4H  pencil  and  smooth  white 
paper  with  hard  surface.  Sharpen  the  pencil  to  a  fine  point. 
At  first,  draw  a  bottom  guide  line  for  letters;  later,  practice 
lettering  without  a  guide  line.  In  forming  the  various  letters 
and  figures  pay  particular  attention  to  the  direction  and  sequence 
of  the  strokes  in  each  letter  and  learn  the  peculiar  characteristics 
of  each.  The  stem  of  a  letter  which  extends  above  or  below 
the  body  of  the  letter  should  not  be  made  too  long  —  a  common 
mistake. 

(a)  Print  the  entire  alphabet  of  lower  case  letters,  grouping 
them  in  five  groups  :  adgq,  bp,  ceos,  hmnu,  and  fijklrtvwxyz. 
(See  p.  25.)  Repeat  this  exercise  several  times. 

(6)  Print  the  capital  letters  of  the  alphabet,  grouping  them  as 
follows:  EFHIKLMNTZ,  AVWXY,  BPR,  CGOQ,  and  SJDU. 
(See  p.  28.)  Repeat  this  exercise  several  times. 

(c)  Practice  making  the  numerals  from  1  to  0.  (See  p.  27.) 

(d)  Rule  bottom  guide  lines  about  a  quarter  of  an  inch  apart, 
and  print  in  single  stroke  lettering,  with  the  letters  spaced  as 
closely  together  as  possible,   the   introductory  note   on  page 
XXVII. 


GROUP  C. 

EXERCISES   IN  CHAINING. 

The  first  six  exercises  of  this  group  offer  the  student  an  opportunity 
to  form  correct  habits  in  the  use  of  the  steel  tape,  and,  by  a  study  of  the 
sources  of  error,  to  learn  what  precautions  must  be  taken  to  attain  a  given 
degree  of  precision.  The  remaining  exercises  involve  special  problems  in 
chaining,  most  of  which  are  based  on  well  known  geometric  constructions. 
If  it  is  necessary  to  omit  any  of  these  latter  problems  in  the  field,  the 
omitted  problems  may  be  given  in  the  class-room  as  blackboard  exercises, 
and  the  corresponding  questions  discussed  by  the  class. 

Exercise  C-l. 
Reading  a  Chain  Tape. 

References:   Page  32,  §  48;  p.  33,  §  50  (a)  (b)  (c)  (d). 

Equipment:   Chain  tape  and  chain  pins. 

Directions:  1.  On  a  level  piece  of  ground,  stick  two  chain  pins 
at  random  about  50  feet  apart.  2.  Measure  the  distance  between 
these  two  pins  to  the  nearest  tenth  of  a  foot.  3.  Repeat  the 
measurement,  the  two  chainmen  interchanging  positions. 

Questions:  1.  Why  should  the  chainman  at  the  end  of  the 
tape  make  the  final  reading?  §  50  (c).  2.  Why  should  the  other 
chainman  read  the  number  on  each  side  of  the  required  reading? 
p.  33.  3.  What  kind  of  tape  may  be  used  to  render  these  pre- 
cautions unnecessary?  §  50  (d).  4.  Does  the  surveyor  use 
decimal  parts  of  a  foot  or  inches?  p.  3.  5.  When  would  it  be 
desirable  to  use  a  tape  graduated  to  inches?  6.  Are  linear 
measurements  in  surveying  ever  made  along  an  inclined  surface? 
p.  2.  7.  What  is  the  equivalent  of  one  vara  in  inches?  p.  3. 
8.  What  is  the  equivalent  of  one  meter  in  feet?  p.  3.  9.  What 
other  units  of  measurements  are  sometimes  used?  p.  3.  10.  Why 
was  66  feet  adopted  as  the  length  of  Gunter's  chain?  p.  3. 
11.  What  is  a  convenient  method  of  converting  hundredths  of  a 
foot  to  fractions  of  an  inch?  p.  3.  12.  What  is  the  difference  be- 
tween Gunter's  chain  and  an  Engineer's  chain?  p.  559.  13.  How 
would  you  record  10  chains  7  links?  p.  33,  §  49.  14.  Compare 
the  three  kinds  of  tapes,  p.  559.  15.  What  are  the  relative 
merits  of  a  chain  and  a  tape?  Remark,  p.  33.  16.  Describe  the 
different  kinds  of  steel  tapes,  and  the  standard  methods  of  gradu- 
ating tapes,  pp.  560,  561. 

6 


EXERCISES   IN   CHAINING.  7 

Exercise  C-2. 

Chaining  Distances  Greater  than  the  Length 
of  the  Tape. 

References:  Page  34,  §  50  (e)  and  (f),  §  51  and  §  52;  p.  37,  §  56, 
1-12. 

Equipment:  Two  range  poles;  steel  tape  and  chain  pins. 

Directions:  1.  Ascertain  just  what  points  to  take  for  the  ends 
of  the  tape.  2.  Set  two  chain  pins  about  300  or  400  feet  apart 
on  comparatively  level  ground.  3.  Chain  the  distance  between 
these  two  pins.  4.  Repeat  the  measurement,  the  two  chainmen 
interchanging  positions.  By  means  of  the  tape  tables  on  pages 
48  and  49  ascertain  whether  the  discrepancy  between  the  two 
measurements  indicates  poor  work  or  good  work. 

Suggestions:  Special  attention  should  be  paid  by  the  instructor  to  the 
method  of  sticking  the  pins  as  this  is  usually  the  source  of  greatest  error  on 
level  ground.  Insist  on  the  use  of  signals,  page  35,  and  caution  men  in 
regard  to  pulling  up  pins  that  mark  the  ends  of  a  line. 

Questions:  1.  What  is  the  approximate  pull  used  in  ordinary 
chaining?  p.  42,  §  65.  2.  Why  should  the  pins  be  stuck  at  right 
angles  to  the  line?  3.  How  are  the  pins  used  to  keep  count  of  tape 
lengths?  4.  How  can  the  head  chainman  keep  himself  approxi- 
mately in  line?  5.  In  accurate  work  what  precaution  should  be 
taken  after  each  pin  is  stuck?  p.  37,  §  56  (12).  6.  If  there  is  a 
slight  difference  between  the  first  and  second  measurements  of  the 
line,  what  is  this  difference  called?  p.  11,  §  20.  7.  If  this  dis- 
crepancy is  small,  is  the  error  of  chaining  necessarily  small? 
p.  11,  §§  20,  21.  8.  If  the  tape  used  in  measuring  is  too  long  or 
too  short,  is  this  a  source  of  constant  error?  p.  10.  9.  Are  the 
errors  from  sticking  the  pins  accumulative  or  compensating? 
p.  11,  also  p.  42,  §  66.  10.  If  in  lining  in,  pins  are  set  as  much  as 
6  inches  first  one  side,  then  the  other  of  the  line,  will  the  resulting 
error  be  comparatively  large  or  small?  p.  41,  §  63,  p.  51,  §  76. 
11.  How  may  the  error  in  chaining  be  expressed  by  a  ratio? 
p.  39,  §  58.  12.  If  a  line  is  measured  with  a  tape  that  is  too  long 
will  the  result  be  too  long  or  too  short,  and  what  is  the  correspond- 
ing algebraic  sign?  p.  39,  §  59.  13.  What  are  some  of  the  things 
a  chainman  should  do?  14.  What  are  some  of  the  things  a  chain- 
man should  not  do?  p.  38.  15.  If  in  chaining  a  line  AB  whose 
true  length  is  400  feet,  the  first  pin  is  stuck  18  inches  to  the  left 


8  EXERCISES    IN   CHAINING. 

of  the  line,  the  second  pin  16  inches  to  the  right,  the  third  pin  24 
inches  to  the  right,  what  would  be  the  difference  between  the  true 
length  and  the  measured  length  of  AB}  provided  no  other  errors 
are  involved?  16.  If  in  measuring  along  a  line  the  end  of  the 
tape  should  fall  at  a  place  where  a  pin  cannot  be  stuck,  as,  for 
example,  in  the  middle  of  a  brook,  how  would  you  proceed? 

Exercise  C-3. 
Chaining  on  a  Slope. 

References:  Page  35,  §  53. 

Equipment:  Steel  tape,  chain  pins,  range  poles,  plumb  bob. 

Directions:  1.  Measure  the  distance  between  two  points  on  a 
comparatively  steep  slope  by  the  second  method,  page  36,  work- 
ing down  hill.  2.  Repeat  the  measurement,  chaining  again 
down  hill,  but  the  two  chainmen  interchanging  positions.  3.  By 
means  of  the  tables  on  pages  48  and  49,  ascertain  whether  the 
discrepancy  between  the  two  measurements  indicates  work  that 
is  excellent,  good,  fair  or  passable. 

Suggestions:  1.  Pay  special  attention  to  throwing  the  weight  of  the  body 
against  the  arm  in  holding  the  down-hill  end  of  the  tape.  p.  36.  2.  If  the 
pin  is  stuck  upright  it  interferes  with  the  plumb  bob  —  one  reason  for  stick- 
ing it  in  slanting  at  right  angles  to  the  line.  3.  A  common  error  is  the  hold- 
ing of  the  down-hill  end  of  the  tape  too  low.  The  instructor,  standing 
opposite  the  middle  of  the  tape,  should  watch  this  at  first.  4.  Three  men 
can  work  to  much  better  advantage  than  two  in  chaining  on  a  slope. 

Questions:  1.  Why  is  it  better  to  chain  down  hill  than  up  hill? 
2.  If  a  line  is  chained  on  the  slope  instead  of  in  horizontal  stretches, 
how  may  the  result  be  corrected?  Page  35,  §  53  (a). 

Exercise  C-4. 
Standardizing  the  Tape. 

References:  Pages  39-44  and  p.  561. 

Equipment:  Steel  tape  to  be  tested ;  scale,  spring  balance,  turn- 
buckles,  thermometer,  magnifying  glass. 

Directions:  Assuming  that  a  permanent  standard  has  already 
been  established,  proceed  as  directed  for  "Testing  the  Tape," 
page  562.  2.  Repeat  the  test  two  or  more  times. 

Suggestion:  Sometimes  in  place  of  a  permanent  standard  such  as  that 
described  on  page  562,  the  tape  is  compared  with  a  standard  tape  of  known 
length,  kept  for  that  purpose. 


EXERCISES   IN    CHAINING. 


FORM  OF   NOTES. 


Tape 
Tested. 

Observed 
Length. 

Temper- 
ature. 

Correction 
for  Temp. 

Corrected 
Length. 

Questions:  1.  What  are  the  usual  standard  temperatures  and 
standard  pulls  for  a  100  foot  steel  tape?  Pages  561  and  42. 
2.  What  is  the  average  change  in  length  for  each  15  degrees  change 
in  temperature?  p.  40,  §  62  (a).  3.  What  is  the  average  change  in 
length  per  15  pounds  pull?  p.  43,  §  69  (7).  4.  Where  can  a  tape 
be  sent  for  standardizing?  p.  561.  5.  What  are  some  of  the  condi- 
tions to  be  fulfilled  in  any  device  for  standardizing  tapes?  p.  561. 
6.  What  was  the  object  in  using  a  steel  strip  for  the  standard  of 
the  Boston  Water  Works?  p.  562.  7.  A  line  measured  with  a 
100  foot  tape  is  found  to  be  826.34  feet  long.  What  was  the  true 
length  of  the  line,  (a)  if  the  tape  was  100.024  feet  long?  (b)  if  the 
tape  was  99.87  feet  long?  8.  Required  to  lay  off  the  distance  of 
784  feet  with  a  tape  (a)  100.04  feet  long;  (b)  99.9  feet  long. 

Exercise  C-5. 
Experiments  with  a  Steel  Tape. 

References:  Page  40,  §  62  (c),  p.  41,  §  64. 

Equipment:  Steel  tape,  scale,  spring  balance,  turn-buckles, 
thermometer,  magnifying  glass,  2  plumb  bobs. 

Directions:  1.  Perform  the  experiment  of  §  62  (c),  p.  40. 
2.  Test  the  length  of  a  tape  first  under  a  12  pound  pull,  then 
under  a  20  pound  pull.  Repeat  several  times.  3.  With  the 
ends  of  the  tape  supported  a  short  distance  above  the  floor  or 
ground,  the  rest  of  the  tape  being  unsupported,  find  the  tension 
required  to  make  the  tape  of  standard  length.  Use  plumb  bobs 
to  mark  the  ends  of  the  tape  and  turn-buckles  to  hold  the  tape 
steady  at  the  standard  pull. 

Questions:  1.  A  line  measured  in  summer  with  a  100  foot 
tape,  70°  F.  temperature,  12  pound  pull  is  found  to  be  438.945 
feet  long;  measured  again  in  winter  at  a  temperature  of  10°  F., 
with  the  same  tape  and  same  pull,  what  should  be  its  length 
(tape  supported  in  both  cases  on  level  supports)?  p.  40,  §  62. 
2.  A  tape  is  100  feet  long,  I  inch  wide,  ^  inch  thick  and  weighs 


10  EXERCISES    IN    CHAINING. 

.0005  pounds  per  inch;  standard  at  62°  F.,  12  pound  pull.  A  line 
measured  when  the  temperature  is  90°  F.  and  the  pull  20  pounds 
with  the  tape  supported  at  the  two  ends  only  is  found  to  be  93.41 
feet  long.  Required  the  corrected  length  of  the  line.  3.  Com- 
pare the  pull  required  to  balance  the  sag  as  obtained  in  the  third 
experiment  above  with  that  obtained  theoretically ^rom  the  for- 
mula at  the  bottom  of  page  41,  using  the  tape  described  in  the 
preceding  question. 

Exercise  C-6. 
Measuring  a  Base  Line. 

References:  Page  57,  §  82. 

Equipment:  Steel  tape,  scale,  spring  balance,  thermometer, 
magnifying  glass  (if  desired  a  turn-buckle  device  for  stretching 
the  tape). 

Directions:  1.  On  a  level  stretch  of  ground  set  stakes  with 
their  tops  on  a  level,  making  a  line  several  hundred  feet  long. 
Measure  the  length  of  this  base  line  a  number  of  times  as  directed 
on  page  57.  2.  Find  the  probable  error  as  explained  on  page  58 
(read  also  pp.  15-19). 

Suggestions:  As  it  will  require  considerable  time  to  set  stakes,  this  may  be 
done  once  for  all  and  the  same  stakes  used  by  different  squads. 

Questions:  1.  What  should  be  the  maximum  discrepancy 
between  two  measurements  of  a  line  1000  feet  long,  that  the  work 
may  be  classed  as  excellent?  pp.  48,  49.  2.  Is  a  large  error  more 
likely  to  occur  from  a  variation  in  temperature  or  a  variation  in 
pull?  p.  43.  3.  Give  the  relative  importance  of  different  sources 
of  error,  p.  43.  4.  State  some  of  the  requirements  correspond- 
ing to  a  ratio  of  precision  of  1/50000.  p.  51.  5.  When  it  is 
impracticable  to  set  stakes  with  their  tops  on  a  level,  how  would 
you  proceed?  p.  57.  6.  How  can  tripods  be  employed  in  chain- 
ing a  base  line  through  thick  underbrush?  p.  58.  7.  Sketch  a 
device  for  supporting  and  stretching  a  tape.  8.  Give  ideal  con- 
ditions for  base  line  measurement.  9.  What  is  the  object  in 
having  the  end  of  the  tape  fall  on  a  different  stake  each  time  a  line 
is  chained?  10.  Describe  other  apparatus  for  measuring  base 
lines,  p.  194.  11.  Give  some  practical  suggestions  for  setting 
supporting  stakes,  protecting  end  hubs,  etc.  p.  57, 


EXEKCISES   IN   CHAINING.    .  11 

Exercise  C-7. 
A  Chain  Survey  of  an  Irregular  Polygon. 

Reference:  Page  56,  §  80. 

Equipment:  Chain  or  tape,  chain  pins,  range  poles,  plumb  bob. 

Directions:  1.  Set  5  stakes  at  random,  forming  an  irregular 
polygon  each  side  of  which  is  at  least  150  feet  long.  2.  Survey 
this  polygon  with  a  tape  as  explained  on  page  56.  3.  Compute 
the  area  of  the  polygon  by  finding  the  area  of  each  of  the  triangles 
into  which  it  is  subdivided  from  formula  12  on  page  408. 

Suggestions:  A  survey  of  some  plot  of  land  having  straight  boundary 
lines  may  be  substituted  if  desired.  For  a  survey  of  a  plot  with  irregular 
boundary  lines  see  page  15  of  this  book. 

Field  Notes:  1.  A  sketch  showing  all  measurements.  2.  The 
computations  for  areas  neatly  arranged. 

Questions:  1.  How  can  the  angles  of  the  polygon  be  found 
from  the  original  measurements?  2.  Give  the  general  method 
for  making  any  chain  survey,  p.  56.  3.  If  in  the  survey  shown 
in  Fig.  80,  p.  56,  it  were  impossible  to  see  all  four  corners  from  any 
one  station,  how  would  you  proceed? 

Exercise  C-8. 

To  Chain  from  a  Given  Point  over  the  Brow 
of  a  Hill  to  Another  Point. 

Reference:  Page  55,  §  79. 

Equipment:  Tape,  chain  pins,  sight  poles,  plumb  bobs. 

Directions:  Set  two  poles,  one  over  the  brow  of  a  hill  from  the 
other,  and  chain  the  distance  between  them,  as  explained  on 
page  55. 

Questions:  1.  Give  two  methods  of  "  ranging  in  "  when  a  valley 
intervenes  between  the  two  points,  p.  56,  §  79  (c).  2.  Give  the 
method  of  chaining  over  a  high  wall.  p.  54.  3.  Give  a  method 
of  chaining  a  line  between  two  points  when  woods  intervene,  p. 54. 


12  EXERCISES   IN  CHAINING. 

Exercise  C-9. 

Laying  Out  a  Right  Angle  with  a  Tape  by 
the  3-4-5  Method. 

Reference:  Page  60. 

Equipment:  Tape  and  chain  pins. 

Directions:  1.  Set  two  pins  in  the  ground  80  feet  apart  and 
with  this  line  as  one  side,  stake  out  an  80  foot  square.  2.  Check 
by  measuring  the  two  diagonals  of  the  square. 

Field  Notes:  Make  a  sketch  showing  each  distance  measured  or 
laid  off  and  the  discrepancy  between  the  two  diagonals. 

Questions:  1.  Explain  the  difference  between  the  methods  of 
laying  out  a  right  angle  with  a  cloth  tape  and  with  a  steel  tape  (a 
100  foot  tape  being  used  in  each  case).  2.  How  would  you  lay 
off  a  right  angle  with  a  50  foot  tape?  3.  If  one  diagonal  of  a 
square  as  staked  out  is  longer  than  the  other  how  would  you  pro- 
ceed to  correct  the  mistake?  4.  If  the  two  diagonals  are  exactly 
equal,  does  this  necessarily  prove  that  the  square  has  been  staked 
out  correctly?  5.  How  closely  should  the  lengths  of  the  two 
diagonals  of  an  80  foot  square  agree  to  indicate  good  work? 
6.  How  would  you  proceed  to  stake  out  the  house  on  page  210, 
using  only  the  tape? 

Exercise  C-10. 

To  Erect  a  Perpendicular  with  a  Tape  at 
Any  Point  in  a  Line. 

Reference:  Pages  61,  62  and  63. 

Equipment:  Tape  and  chain  pins. 

Directions:  1.  Set  two  pins  at  random  and  at  one  of  them  erect 
a  perpendicular  to  the  line  between  them  by  the  method  of  §  85  (b), 
p.  61.  2.  Check  by  the  3-4-5  method. 

Field  Notes:  Make  a  sketch  showing  all  measurements. 

Questions:  1 .  What  is  the  difference  between  the  methods  used 
for  geometrical  constructions  in  drafting  and  those  used  for 
the  same  constructions  in  chaining?  Illustrate  by  sketches. 
2.  What  method  in  chaining  corresponds  to  erecting  a  perpen- 
dicular by  intersecting  arcs  and  how  may  the  perpendicular 
erected  by  this  method  be  checked  by  the  use  of  the  same  method? 
p.  61.  3.  Illustrate,  by  sketches,  methods  of  dropping  a  perpen- 
dicular to  a  given  line  from  any  given  point,  p.  62. 


EXERCISES   IN  CHAINING.  13 

Exercise  C-ll. 
To  Run  One  Line  Parallel  to  Another  Line. 

Reference:  Page  62  and  page  63. 

Equipment:  Tape  and  chain  pins. 

Directions:  Assume  three  points  at  random  and  through  one  of 
them  establish  a  line  parallel  to  the  line  between  the  other  two, 
using  two  different  methods. 

Field  Notes:  Make  a  sketch  showing  all  measurements. 

Question:  Discuss  the  advantages  and  disadvantages  of  the 
three  methods  given  on  page  63. 

Exercise  C-12. 

To  Measure  between  Two  Points  when  a  Corner 
of  a  Building  Intervenes. 

Reference:  Page  64,  §  87  (a). 

Directions:  1.  Assume  two  points  at  least  40  to  60  feet  apart 
and  imagine  a  corner  of  a  building  to  intervene.  Find  the  dis- 
tance between  the  two  points  by  one  of  the  methods  explained  on 
page  64  and  check  the  result  by  the  other  method.  2.  Check 
also  by  a  direct  measurement. 

Suggestion:  Having  completed  the  exercise  with  an  imaginary  obstacle, 
it  is  well  to  repeat  the  work  with  the  corner  of  a  real  building  intervening 
between  the  two  given  points. 

Field  Notes:  Make  a  sketch  showing  all  measurements  made 
during  the  exercise,  and  the  final  results. 

Exercise  C-13. 
To  Measure  to  an  Inaccessible  Point. 

Reference:  Page  64,  §  87  (b). 

Equipment:  Chain  and  chain  pins. 

Directions:  1.  Set  two  stakes  or  pins  about  200  feet  apart. 
2.  Find  the  distance  between  the  two  points  by  two  different 
methods.  3.  Check  results  by  direct  measurement. 

Questions:  1.  Could  the  methods  used  in  transit  work  (p.  222, 
§  277  (c) )  be  used  in  chaining?  2.  Explain  at  least  two  other 


14  EXERCISES    IN    CHAINING. 

methods  that  might  be  used  with  a  tape.  §  87  (c).  3.  Describe  a 
rough  method  of  measuring  the  height  of  an  inaccessible  point. 
§  87  (d).  4.  Describe  at  least  two  methods  of  prolonging  a 
straight  line  through  an  obstacle  using  only  the  tape.  p.  66.  (If 
time  permits  this  may  be  done  in  the  field  as  an  additional  exer- 
cise.) 5.  Show  by  a  sketch  one  method  of  measuring  between 
two  inaccessible  points.  §  87  (e). 

Field  Notes:  1.    A  sketch  showing  all  measurements.     2.    Arith- 
metical work  neatly  arranged. 


Exercise  C-14. 

To  Measure  the  Angles  of  a  Triangle  with 
a  Tape. 

References:  Page  63,  §  86,  and  pages  458-460. 

Equipment:  Tape  and  chain  pins. 

Directions:  Set  three  stakes  or  chain  pins  at  random  to  form  a 
triangle  with  no  side  less  than  100  feet  long.  2.  Measure  each 
interior  angle  of  the  triangle  with  the  tape  using  the  tangent 
method.  3.  Repeat  the  problem  using  the  chord  method. 

Suggestions:  1.  Take  a  reasonably  long  distance  for  the  base  in  the 
tangent  method  and  the  radii  in  the  chord  method.  2.  Pay  particular 
attention  to  lining  in  —  the  errors  are  chiefly  here. 

Field  Notes:  1.  A  sketch  of  the  triangle  showing  all  measure- 
ments for  the  first  method ;  a  similar  sketch  for  the  second  method. 
2.  All  arithmetical  work  neatly  arranged.  3.  A  comparison  of 
results  of  the  first  and  second  methods.  4.  Actual  error  in  the 
sum  of  the  angles. 

Questions:  I.  Illustrate  how  to  measure  angles  of  various  sizes 
from  0°  to  360°  by  the  tangent  method;  by  the  chord  method. 
2.  What  is  the  most  convenient  base  or  radius?  3.  Upon  what 
does  the  accuracy  of  the  tangent  method  depend?  4.  When  is  it 
advantageous  to  use  the  chord  method  instead  of  the  tangent 
method?  5.  Explain  the  sine  and  cosine  method,  p.  63. 


EXERCISES   IN    CHAINING.  15 


Exercise  C-15. 

A  Chain  Survey  of  a  Plot  of  Ground  with  Irregular 
Boundary  Lines  and  Containing  Buildings. 

References:  Page  56,  §  80,  also  pp.  138  to  140. 

Equipment:  Steel  tape,  chain  pins,  stakes,  hatchet  and  range 
poles. 

Directions:  Make  a  survey  of  a  small  plot  of  ground  in  which 
some  of  the  boundary  lines  are  curved  or  irregular.  There  should 
also  be  some  buildings  to  be  located.  Establish  a  network  of 
triangles  for  reference  lines  as  explained  on  page  56,  §  80  (c),  and 
locate  the  different  details  as  explained  on  pages  138-140. 

Suggestions:  If  desired  this  exercise  may  be  conducted  as  a  recitation, 
the  different  methods  being  discussed  by  the  class  as  a  whole,  or  by  each 
squad,  and  each  method  illustrated  by  sketches  on  the  blackboard  or  in  the 
note-book. 

Field  Notes:  1.  A  complete  sketch  showing  all  measurements 
made  in  the  field.  2.  Computations  for  area  neatly  arranged. 

Questions:  1.  Give  the  methods  of  locating  a  point  from  two 
given  points  by  linear  measurement  only.  p.  4.  2.  Explain 
method  of  locating  a  building  by  means  of  offsets,  p.  138,  §  198  (a). 
3.  Explain  the  method  of  locating  a  regular  curve  by  offsets. 
§  198  (b).  4.  Explain  the  method  of  locating  an  irregular  out- 
line like  the  bank  of  a  stream,  by  linear  measurements  only. 
5.  What  three  points  must  be  kept  in  mind  in  using  the  offset 
method?  §  198  (d).  6.  Explain  the  "plus  system"  often  used 
in  the  offset  method.  Note,  p.  139.  7.  Explain  how  to  locate  a 
building  by  three  measurements,  one  of  which  is  a  tie  line. 
Figure  199  (a).  8.  Is  it  necessary  that  the  tie  line  should  have 
one  end  at  some  point  on  the  building?  p.  140.  9.  Explain  how 
to  locate  a  building  by  two  pairs  of  intersecting  measurements. 
Figure  199  (b).  10.  Explain  the  use  of  tie  lines  in  getting  the 
directions  of  fences.  §  199  (c).  11.  How  may  the  area  of  the 
plot  surveyed  be  computed?  pp.  410-413.  (If  time  permits, 
compute  the  area  of  the  plot  surveyed.) 


16  EXERCISES    IN    CHAINING. 

Exercise  C-16. 
Discussion  of  the  Errors  in  Linear  Measurements. 

References:     Chapter  V,  pages  39  to  53. 

Questions:  1.  What  are  the  four  general  sources  of  error  in 
chaining?  p.  39.  2.  How  is  an  error  expressed  by  a  ratio?  3.  If 
a  line  is  measured  with  a  tape  that  is  too  short,  will  the  result  be 
too  short  or  too  long,  and  what  is  the  corresponding  algebraic 
sign?  4.  Why  is  the  error  in  the  length  of  a  chain  likely  to  be 
relatively  greater  than  that  in  a  tape?  5.  Show  by  an  illustra- 
tion how  to  apply  a  correction  for  an  error  in  the  length  of  a 
tape  when  chaining  between  two  points;  when  laying  off  a 
given  distance,  p.  40.  6.  How  can  an  error  due  to  the  tape 
not  being  horizontal  be  eliminated?  7.  When  is  the  error  due 
to  temperature  plus,  and  when  minus?  8.  What  is  the  approxi- 
mate change  in  the  length  of  a  100-foot  steel  tape  for  a  change 
in  temperature  of  90°  F.?  9.  When  should  temperature  be 
taken  into  account  and  when  not?  10.  What  precautions  are 
often  taken  in  base  line  measurement  to  eliminate  the  error  due 
to  temperature?  11.  What  approximate  rate  of  change  may  be 
remembered  for  a  100-foot  tape?  12.  If  the  length  of  a  city 
block  is  measured  in  summer  and  then  again  in  winter  with  the 
same  tape,  what  discrepancy  due  to  change  in  temperature 
may  be  expected?  13.  Describe  an  experiment  which  may 
be  tried  to  show  the  effect  of  a  small  change  in  temperature 
upon  the  length  of  a  steel  tape.  14.  What  is  meant  by  the 
error  in  alignment,  and  is  this  source  of  error  relatively  important? 
p.  41.  15.  In  ordinary  chaining,  is  it  necessary  for  the  transit- 
man  to  line  the  chainman  in  with  the  instrument?  16.  Is  an 
error  due  to  sag  plus  or  minus?  17.  What  three  ways  are  there 
of  eliminating  the  error  due  to  sag?  18.  How  may  the  error  due 
to  uneven  pull  be  eliminated?  p.  42.  19.  How  may  the  errors  in 
marking  tape  lengths  be  reduced?  20.  In  what  kind  of  work  is 
this  source  of  error  the  greatest?  21.  Name  four  common 
mistakes  made  in  reading  tapes.  22.  In  extremely  accurate 
work,  what  precautions  may  be  taken  in  reading  the  tape? 

23.  Summarize  the  eleven  sources  of  errors  in  chaining,  p.  43. 

24.  From  what  two  sources  are  errors  compensating?     25.    What 
errors  are  always  plus?      26.    Discuss  the  relative  importance 
of  the  sources  of  errors,  pointing  out  from  which  sources  impor- 


EXERCISES   IN   CHAINING.  17 

tant  errors  are  most  likely  to  occur,  and  what  sources  may 
be  neglected  in  ordinary  work.  27.  In  judging  the  relative 
importance  of  errors,  what  points  should  be  kept  in  mind?  p.  44. 

28.  What  largely  determines  limits  of  error  in  a  given  survey? 

29.  Should  all  measurements  in  the  same  survey  be  made  with 
equal  care?     30.   In  general,  what  distances  should  be  measured 
carefully  and  what  less  carefully?  p.  45.     31.    What  are  some 
of  the  conditions  that  affect  the  accuracy  of  chaining?     32.    If 
the  accidental  errors  amount  to  0.02  foot  for  100  feet  in  using  a 
100-foot  tape,  what  would  be  the  probable  error  in  measuring 
a  line  900  feet  long?     33.    Give  the  general  rule  for  finding  the 
probable  error.     34.    Why  is  not  the  discrepancy  between  two 
measurements  of    the  same   line    affected   by  constant  errors? 
35.    If  the  discrepancy  between  two  measurements  of  the  length 
of  a  tape  is. 0.01,  what  is  it  likely  to  be  between  two  measure- 
ments of  a  line  sixteen  tape  lengths  long?     36.    What  can  you 
say  regarding  the  value  of  the  formula  at  the  top  of  page  46? 
37.    Discuss  the  remark  at  the  top  of  page  46,  and  explain  why 
the   last   sentence   in   that   remark   is   true.     38.    Explain   the 
first  method  of  determining  a  coefficient  of  precision  for  chaining. 

39.  Explain  a  method  which  may  be  used  for  ordinary  chaining. 

40.  A  line  is  chained  twice  under  favorable  conditions,  measure- 
ments being  made  with  an  ordinary  chain,  plumb-bob,  chain- 
pins  and   average   speed.     The   two  results  were,  respectively, 
618.1,  618.3.     Would  the  work  be  classed  excellent,  good,  or 
fairly  good?     (See  Table  1,  p.  48.)     41.    If  a  steel  tape  had  been 
used  in  place  of  a  chain,  other  conditions  being  the  same,  what 
would  be  the  allowable  discrepancy  in  good  work  between  the 
two    measurements    in    the    preceding    question?     42.    Apply 
Table  2,  page  49,  to  questions  40  and  41.     43.  Explain  how  the 
table  on  page  51  may  be  used  to  indicate  the  precautions  which 
are    necessary  to    attain    certain  degrees    of   precision,   p.    52. 
44.    Discuss    the  matter    of    combining    errors    from  different 
sources,  p.  52. 


GROUP  T. 

EXERCISES  IN  THE  USE  OF  THE  TRANSIT. 

The  exercises  in  this  group  offer  the  student  an  opportunity  to  form 
correct  habits  in  manipulating  the  transit  and  in  reading  angles.  As  habits 
formed  early  in  the  course  are  likely  to  cling  to  one  long  after  graduation, 
and  as  the  transit  is  perhaps  the  most  important  instrument  used  in  survey- 
ing, no  suggestion,  however  trivial  it  may  seem,  should  be  ignored  if  it  is 
likely  to  help  one  to  become  skilful  and  accurate  in  the  use  of  the  transit. 

Exercise  T-l. 
Setting  up  a  Transit. 

References:  Pages  84-89,  §§  109-115. 

Equipment:  A  transit  for  each  student,  or  as  many  transits  as 
are  available. 

Directions:  1.  Set  up  the  transit  on  comparatively  level 
ground,  paying  special  attention  to  the  suggestions  on  page  87. 
2.  Repeat  the  work,  selecting  a  place  on  a  side  hill. 

Suggestions:  At  the  beginning  of  the  exercise,  it  is  well  for  each  instructor 
to  show  his  squad  how  to  set  up  a  transit,  emphasizing  at  the  same  time  the 
importance  of  the  suggestions  on  page  87,  §  114.  The  members  of  the  squad 
may  then  be  drilled  individually  under  close  supervision  of  the  instructor, 
several  transits  being  used  simultaneously,  if  possible. 

If  this  exercise  is  given  before  the  exercises  in  the  use  of  the  level,  it  is 
well  for  the  instructor  to  explain  briefly  the  principal  parts  of  the  telescope 
(see  photograph,  page  551),  and,  if  thought  best,  to  add  to  the  questions 
given  below  those  on  pages  96  and  97  of  this  book. 

Questions:  1.  Give  some  of  the  precautions  to  be  observed  (a) 
in  the  use  of  clamps  and  screws;  (b)  in  the  treatment  of  lenses; 
(c)  in  standing  a  transit  up  on  a  floor,  p.  84.  2.  Give  pre- 
cautions taken  in  carrying  a  transit,  p.  85.  3.  Give  other 
precautions,  pp.  607-609.  4.  Tie  a  sliding  knot  as  described  on 
p.  85.  (If  the  knot  slides  too  freely,  take  an  extra  turn  of  the 
string  about  the  hook.)  5.  How  are  the  cross-hairs  brought  in 
focus?  p.  85.  6.  Give  the  rule  for  focusing  the  object  glass  on 
distant  objects,  p.  86.  (If  desired,  the  theory  of  lenses 
(pp.  545-549)  and  the  construction  of  the  telescope  (pp.  549-558) 
may  be  studied  in  connection  with  Questions  5  and  6.)  7.  Give 
suggestions  for  sighting  the  telescope,  p.  85,  §  111.  8.  Give  some 

18 


EXERCISES   IN    THE   USE    OF   THE   TRANSIT.      19 

practical  suggestions  for  manipulating  the  tripod,  p.  86,  §§  113, 
114.  9.  Give  suggestions  for  leveling  up.  p.  88.  10.  Explain 
how  the  telescope  level  is  sometimes  used  for  leveling  up.  p.  89. 
11.  If  the  plumb-bob  is  as  much  as  i  to  ^  of  an  inch  off  the  tack, 
how  much  will  this  affect  an  angle  if  sights  are  450  feet  long?  p.  89 
and  p.  105,  §  147.  12.  Give  some  points  to  remember  in  leveling 
up.  p.  89,  §  115. 

Exercise  T-2. 

Prolonging  a  Straight  Line. 

Reference:  Pages  90-93,  §§  116-122. 
Equipment:  Transit,  hatchet,  and  stakes. 

.Directions:  1.  Set  two  stakes  at  random,  at  least  200  feet  apart, 
in  such  a  place  that  the  line  between  them  can  be  prolonged 
another  200  feet.  2.  Set  up  over  the  end  of  the  line  to  be  pro- 
longed, and  set  a  third  stake  in  line  about  200  feet  away,  using  the 
method  of  double  reverse,  p.  92.  3.  Set  up  over  the  other  end  of 
the  original  line  and  see  if  all  three  stakes  are  in  line. 

Suggestion:  Drive  the  stakes  only  part  way  into  the  ground  so  that  they 
may  be  pulled  up  easily.  Mark  the  exact  points  with  a  small  lead-pencil 
cross. 

The  upper  clamp  should  be  set  once  for  all  at  the  beginning  of  the  exercise, 
and  left  undisturbed  during  the  remainder  of  the  exercise.  The  student 
should  then  work  wholly  with  ihelower  clamp  and  corresponding  slow  motion 
screw,  and  thus  become  accustomed  to  using  them  for  backsighting .  Not 
until  Exercise  T-4  should  he  concern  himself  with  the  use  of  the  upper 
clamp  and  the  corresponding  slow  motion  screw. 

It  may  be  well,  at  the  close  of  the  exercise,  for  the  instructor  to  explain 
briefly  by  means  of  the  figures  on  pages  588  and  590  what  errors  of  adjust- 
ment may  be  eliminated  by  reversing  in  azimuth  and  altitude. 

Field  Notes:  A  short  statement  of  the  work  and  of  the  dis- 
crepancy, if  any,  found  in  the  final  check  of  the  third  step  above. 

Questions:  Define  backsight,  foresight,  permanent  backsight, 
and  permanent  foresight,  p.  90.  2.  Explain  the  use  of  the  upper 
and  lower  clamps  and  the  corresponding  tangent  screws,  p.  91, 
§  119,  pp.  563-566.  3.  Give  signals  for  lining  in.  p.  146.  4.  Ex- 
plain the  method  of  reversing  in  azimuth  and  altitude ;  what  are 
other  synonymous  terms?  p.  92.  5.  In  setting  up  to  prolong  a 
straight  line,  what  precaution  may  be  taken?  p.  89  (14);  also 
note,  p.  92.  6.  What  four  methods  are  there  for  prolonging  a 
straight  line? 


20      EXERCISES   IN   THE   USE   OF   THE   TRANSIT. 

Exercise  T-3. 
Balancing  in  a  Transit. 

References:  Page  93  and  page  201. 

Equipment:  Transit,  hatchet,  stakes,  and  sight  poles. 

Directions:  Set  two  stakes  several  hundred  feet  apart,  and 
balance  in  the  transit  about  half  way  between  them  as  explained 
on  page  201.  2.  When  the  transit  is  apparently  on  line,  test  by 
the  method  of  double  reverse. 


Exercise  T-4. 
Beading  the  Limb  of  a  Transit. 

References:  Pages  67-75. 

Equipment:  A  transit  for  each  student,  or  as  many  transits  as 
are  available. 

Directions:  1.  Clamp  the  plates  of  a  transit  at  random,  read 
the  number  of  degrees  (clockwise),  estimate  the  number  of 
minutes,  and  record  the  total  reading.  Pay  no  attention  to  the 
vernier  reading.  .  2.  Record  the  correct  reading  as  given  by  the 
instructor  (who  will  read  the  vernier).  3.  If  the  transit  has  two 
verniers  180  degrees  apart,  repeat  for  the  reading  across  the  circle. 
4.  Repeat  the  whole  exercise  until  from  6  to  10  different  readings 
have  been  made  and  recorded  by  each  student. 

Suggestions:  If  a  number  of  transits  are  available  for  each  squad,  they  may 
be  set  up  within  a  few  feet  of  each  other,  and  the  plates  of  each  transit  set  at 
random  by  the  instructor.  Each  student  may  then  read  in  turn  the  limb  of 
each  transit.  No  vernier  readings  should  be  permitted,  as  the  object  of  the 
exercise  is  to  make  each  student  thoroughly  familiar  with  the  method  of 
reading  the  limb  before  he  undertakes  to  read  the  vernier.  After  the  student 
has  become  accustomed  to  reading  the  angles  clockwise,  he  may  be  drilled  in 
reading  the  angles  counter-clockwise. 

At  the  beginning  of  the  exercise  it  is  well  for  the  instructor  to  explain 
briefly  how  the  upper  and  lower  plates  may  be  turned  independently  or 
together,  and  to  illustrate  the  use  of  the  upper  and  the  lower  clamps  and 
the  corresponding  slow  motion  screws.  The  photograph  on  page  565  should 
be  useful  in  this  connection. 

If  transits  with  special  forms  of  numbering  are  available,  as,  for  example, 
one  like  that  described  in  Article  95  (d),  page  73,  a  special  drill  should  be 
given  in  reading  such  instruments. 


EXERCISES    IN    THE   USE    OF    THE   TRANSIT.      21 


FORM   OF   NOTES. 

Number  of  Reading.         Value.       Instructor's  Reading. 

1  37°  15'  37°  18' 

2  108°  40'  108°  38'   ' 

Questions:  1.  Which  plate,  the  limb  or  that  carrying  the 
vernier,  must  necessarily  turn  when  the  telescope  is  moved  side- 
wise?  pp.  67,  563.  2.  Give  the  three  common  systems  of  num- 
bering the  limb  gradations,  p.  67.  3.  Give  four  common  methods 
of  subdividing  the  degree  on  the  limb.  p.  68.  4.  Give  the  three 
steps  in  reading  an  angle,  p.  68.  5.  In  which  step  are  important 
mistakes  liable  to  occur?  Remark,  p.  68.  6.  Explain  what  is 
meant  by  reading  an  angle  clockwise  and  counter-clockwise 
right  and  left  (p.  68),  and  why  are  the  first  two  terms  preferable 
to  the  last  two  terms?  Remark,  p.  69.  7.  Give  general  method 
of  reading  a  limb.  §  91  (b),  p.  68.  8.  Give  common  mistakes 
in  reading  a  limb.  p.  69.  9.  If  angles  are  always  measured 
clockwise,  what  system  of  numbering  is  best  for  the  transit  (p.  71) 
and  how  many  rows  of  numbers  would  be  needed?  p.  67.  10.  In 
measuring  angles  clockwise,  which  row  of  numbers  on  page  70  is 
ignored?  11.  Why  is  the  portion  of  the  limb  near  the  180-degree 
mark  a  place  where  mistakes  are  liable  to  occur?  p.  71,  §  94  (b). 
12.  Why  is  it  important  to  check  readings  by  estimating  angles 
with  the  eye?  p.  71,  §  94  (b).  13.  What  mistake  is  illustrated 
by  most  of  the  incorrect  readings  on  page  70?  p.  71,  §  94  (c). 
14.  What  mistake  is  illustrated  by  the  reading  of  171°  30'  in  place 
of  191°  30'?  p.  70,  §  94  (c).  15.  If  a  transit  has  only  one  row  of 
numbers  (clockwise),  and  it  is  desired  to  read  an  angle  counter- 
clockwise, how  would  you  proceed?  §  94  (d),  p.  71.  16.  If  a 
transit  has  only  one  row  of  numbers,  and  that  is  the  half-circle 
system,  how  would  you  read  an  angle  clockwise  which  is  greater 
than  180°?  p.  73,  §  95  (c)  and  (d).  17.  When  gradations  are 
numbered  by  a  combination  of  the  full-circle  and  quadrant  sys- 
tems, what  is  a  common  mistake?  p.  75,  §  96  (b),  and  at  what 
two  points  on  the  limb  are  mistakes  most  likely  to  occur? 
(Bottom  of  p.  75.) 

Note:  As  a  result  of  this  exercise  two  things  should  be  impressed  upon 
the  mind  of  the  student,  first  the  importance  of  reading  the  limb  correctly 
before  attempting  to  read  the  vernier,  and,  second,  the  closeness  with  which 
an  angle  may  be  read  without  the  use  of  a  vernier. 


22      EXERCISES   IN   THE   USE   OF   THE   TRANSIT. 

Exercise  T-5. 
Beading  Angles;  Limb  and  Vernier. 

References:  Pages  76-83. 

Equipment:  A  transit  for  each  student,  or  as  many  transits  as 
are  available;  preferably  transits  should  read  to  minutes. 

Directions:  1.  Clamp  the  plates  of  a  transit  at  random,  and 
read  both  the  limb  and  vernier  clockwise,  recording  the  total 
reading.  2.  Record  the  correct  reading  as  given  by  the  instructor. 
3.  Repeat  for  the  vernier  across  the  circle.  4.  Repeat  the  whole 
exercise  until  from  six  to  ten  readings  have  been  made  and 
recorded  by  each  student. 

Suggestions:  Several  transits  may  be  used  by  each  squad  as  in  the  preced- 
ing exercise.  It  is  well,  however,  to  confine  the  work  to  transits  reading  to 
minutes  until  the  method  is  thoroughly  understood,  then  transits  reading  30, 
20,  or  10  seconds  may  be  used.  Finally,. students  should  be  drilled  in  read- 
ing angles  counter-clockwise. 

FORM  OF  NOTES. 
Same  as  that  for  the  preceding  exercise. 

Questions:  1.  What  is  the  principle  of  the  vernier?  pp.  538,  539. 
2.  What  is  the  difference  between  direct  and  retrograde  verniers? 
p.  540.  3.  Explain  how  to  determine  the  smallest  reading  or 
least  count  of  a  vernier,  p.  540;  also  p.  76,  §  97  (c).  4.  In  the 
vernier  reading  to  minutes,  how  large  an  arc  is  covered  by  the 
space  that  is  called  a  minute?  p.  76,  §  97.  5.  Give  the  general 
method  of  reading  a  vernier.  §  98.  6.  Which  side  of  a  double 
vernier  should  be  read?  §  99.  7.  Why  should  the  vernier  reading 
be  estimated  from  the  limb  before  the  vernier  is  read?  §  99  (2). 
8.  How  many  marks  should  be  examined  closely  in  reading  the 
vernier?  §  99  (3).  9.  When  may  an  angle  be  read  to  30  seconds 
on  a  vernier  reading  to  minutes,  and  what  is  the  greatest  error 
involved  in  reading  such  a  vernier?  §  99  (3).  10.  What  pre- 
caution should  be  used  in  setting  a  vernier?  §  99  (4).  11.  When 
there  are  two  verniers  180°  apart,  which  is  ordinarily  used?  §  99. 
12.  What  are  some  of  the  common  mistakes  in  reading  verniers? 
p.  77.  13.  Describe  at  least  three  different  verniers,  each  of 
which  reads  to  minutes?  pp.  78,  79.  14.  Describe  a  common 


EXEECISES    IN    THE   USE    OF    THE   TRANSIT.       23 

form  of  vernier  reading  to  30  seconds,  p.  80.  15.  Describe  a 
common  form  of  vernier  reading  to  20  seconds,  p.  81.  16.  De- 
scribe a  common  form  of  vernier  reading  to  10  seconds,  p.  82. 
17.  Describe  some  special  forms  of  verniers,  p.  83. 

Note:  Different  forms  of  verniers  may  be  assigned  to  students  to  be  drawn 
on  paper  outside  of  the  regular  exercise. 


Exercise  T-6. 
Measuring  Horizontal  Angles  with  a  Transit. 

References:  Pages  93-98,  §§  125-133. 

Equipment:  Transit,  stakes,  hatchet,  and  sight  poles. 

Directions:  1.  Set  four  stakes  ^4,  B,  D,  and  E,  at  random  to  form 
an  irregular  polygon,  no  side  of  which  is  less  than  150  feet  in 
length.  2.  Set  a  stake  C  near  the  center  of  this  polygon.  3.  Set 
up  the  transit  over  C,  and  measure  in  succession  the  horizontal 
angles  ACB,  BCD,  DCE,  and  EC  A,  all  measured  clockwise.  Make 
a  sketch  showing  the  values  of  the  angles.  4.  Check  by  comparing 
the  sum  of  the  four  angles  with  360°. 

Questions:  1.  Give  the  general  method  of  measuring  horizontal 
angles,  p.  93.  2.  Which  clamp  and  tangent  screw  is  used  for 
each  operation?  Bottom  of  p.  93,  top  of  p.  94.  3.  Explain  the 
difference  between  taking  the  angles  to  the  right  and  to  the  left, 
p.  94.  4.  Explain  how  a  number  of  angles  may  be  taken  from 
the  same  backsight,  p.  94.  5.  Is  the  vernier  always  set  at  0 
before  measuring  an  angle?  p.  94.  6.  If  there  are  two  verniers, 
which  is  used?  p.  95.  7.  Why  form  the  habit  of  estimating  the 
angles  by  eye?  p.  95.  8.  Precautions  to  take  after  backsighting. 
p.  95.  9.  Precautions  to  take  in  measuring  a  large  number  of 
angles  from  the  same  backsight,  p.  95,  §  129  (6),  (7),  (8).  10.  In 
taking  angles  clockwise,  is  it  necessary  to  turn  the  telescope  clock- 
wise? 11.  Name  some  of  the  sources  of  error  in  measuring  the 
horizontal  angles,  p.  96.  12.  Give  some  suggestions  for  using  the 
vernier  in  reading  the  angles,  p.  96.  13.  Name  some  common 
mistakes  in  reading  angles,  p.  97.  14.  Relative  importance  of 
errors,  p.  104.  15.  Relative  importance  of  error  in  setting  up 
the  transit,  p.  104.  16.  If  a  pole  is  f  inch  in  diameter  and  is 
held  100  feet  from  the  transit,  what  would  be  the  angular  error 
caused  by  bringing  the  vertical  cross-hair  to  coincide  with  the  edge 


24      EXERCISES   IN    THE    USE    OF   THE    TRANSIT. 

of  the  pole  instead  of  with  its  center?  Bottom  p.  105.  17.  Is  the 
difference  between  the  sum  of  the  four  angles  and  360°  the  true 
error  of  that  sum  or  simply  a  discrepancy?  p.  414,  §  24  (b). 
18.  How  would  you  distribute  this  error?  p.  14,  §  24  (c).  19.  If 
two  angles  ACB  and  BCD  were  measured  separately,  and  then 
checked  by  measuring  ACD,  would  the  difference  between  the 
sum  of  the  first  two  angles  and  the  measured  value  of  ACD  be  a 
true  error,  or  simply  a  discrepancy,  and  how  would  it  be  dis- 
tributed? §  24  (d).  20.  What  method  corresponding  to  the 
work  done  in  this  exercise  is  sometimes  used  in  work  of  high 
precision?  p.  100,  §  139. 


Exercise  T-7. 
Practice  in  Doubling  Horizontal  Angles. 

Reference:  Page  99,  §  138. 

Equipment:  Same  as  for  the  preceding  exercise. 

Directions:  Repeat  the  preceding  exercise,  but  double  each 
angle  as  explained  in  §  138. 

Questions:  1.  Explain  the  method  of  measuring  angles  by 
repetition,  p.  99.  2.  What  is  the  chief  precaution  necessary  in 
manipulating  clamps  and  tangent  screws  when  repeating  an 
angle?  p.  100.  3.  When  is  it  necessary  to  add  multiples  of  360°? 
Illustrate  how  this  is  done.  4.  Explain  how  to  lay  off  an  angle 
accurately,  p.  101,  §  142;  also  p.  218. 

Exercise  T-8. 
Measuring  Vertical  Angles  with  a  Transit. 

Reference:  Page  98,  §  135. 

Equipment:  Transit,  stakes,  and  hatchet. 

Directions:  1.  Drive  two  stakes  A  and  B  about  200  feet  apart, 
B  being  considerably  lower  than  A.  Set  up  over  A  and  measure 
the  vertical  angle  which  the  line  of  sight  from  the  transit  to  B 
makes  with  the  horizontal.  2.  Assume  some  well-defined  point 
at  least  50  feet  above  the  ground  and  200  feet  from  the  transit; 
call  this  point  C,  and  measure  the  angle  which  the  line  of  sight 


EXERCISES    IN    THE   USE    OF   THE   TRANSIT.       25 

from  the  transit  to  C  makes  with  the  horizontal.  3.  Measure 
the  vertical  angle  between  the  lines  of  sight  to  B  and  to  C.  Make 
a  sketch  showing  the  values  of  all  angles.  4.  Check  by  compar- 
ing the  last  angle  measured  with  the  sum  of  the  other  two  angles. 
Questions:  1.  How  should  the  vertical  arc  be  adjusted,  assum- 
ing that  the  transit  is  in  adjustment  otherwise?  p.  98,  §  135. 
2.  How  would  you  proceed  if  neither  the  vertical  arc  nor  the 
corresponding  vernier  were  adjustable?  3.  What  is  the  "index 
error,"  and  how  are  the  algebraic  signs  applied  to  it?  p.  98.  4.  In 
measuring  the  vertical  angles  as  directed  above,  where  is  the 
vertex  of  the  angle?  5.  If  it  were  required  to  measure  a  vertical 
angle,  one  side  of  which  was  determined  by  two  points  on  the 
ground,  how  would  you  proceed,  assuming  that  all  points  are 
accessible?  6.  Is  it  possible  to  double  a  vertical  angle  with  a 
transit  as  ordinarily  made?  7.  How  can  a  transit  be  made  so 
that  it  will  be  possible  to  double  vertical  angles? 


Exercise  T-9. 
To  Find  the  Intersection  of  Two  Lines  of  Sight. 

Reference:  Page  202. 

Equipment:  Transit,  stakes,  hatchet,  wire  brads,  short  pieces  of 
string. 

Directions:  1.  Set  four  stakes  at  random  to  form  a  polygon,  no 
side  of  which  is  less  than  150  feet  in  length.  2.  Find  the  inter- 
section of  the  diagonals  of  this  quadrilateral  as  explained  in  §  257. 

Questions:  1.  Explain  the  method  of  referencing  a  point.  §259. 
2.  Give  other  methods  of  referencing  a  point,  p.  54.  3.  How 
would  you  reference  a  point  for  setting  a  merestone?  p.  203,  §  259. 
Illustration.  4.  Give  two  methods  of  referencing  a  line.  §  260. 
5.  Explain  the  importance  of  referencing  at  least  one  line  in  a 
survey.  §  260.  Remark. 


26       EXERCISES   IN    THE   USE   OF   THE   TRANSIT. 

Exercise  T-10. 

To  Establish  a  Line  of  Sight  Parallel  to  a  Fence 
or  to  a  Building. 

Reference:  Page  201,  §  256. 

Equipment:  Transit,  tape,  stakes,  hatchet,  sight  pole. 

Directions:  1.  Assume  a  station  about  three  feet  from  a  fence 
or  a  building.  2.  Set  the  transit  over  the  station  and  establish 
a  line  of  sight  parallel  to  the  fence  or  to  the  building  as  directed 
on  page  201. 

Field  Notes:  Make  a  sketch  showing  the  fence  or  building,  the 
transit  line  and  the  distance  used.  Describe  the  method  referring 
to  the  sketch  in  order  to  make  it  plain. 

Questions:  1.  What  method  would  you  use  when  the  parallel 
lines  are  a  considerable  distance  apart?  p.  224,  §  278  (b). 


Exercise  T-ll. 

To  Measure  the  Angle  Formed  by  Two  Intersecting 
Lines  without  Setting  Up  over  Either  Line. 

Reference:  Page  202,  §  258. 

Equipment:  Transit,  tape,  hatchet,  stakes,  sight  pole,  pieces  of 
string. 

Directions:  Measure  the  angle  at  any  place  where  two  definite 
fence  lines  meet,  choosing  preferably  a  corner  where  the  transit 
cannot  be  set  up  inside  of  the  fence  line,  using  the  method  of 
§258. 

Suggestion:  If  it  is  inconvenient  to  use  actual  fence  lines,  drive  three 
stakes  to  form  a  triangle  no  side  of  which  is  less  than  200  feet  in  length,  and 
measure  the  interior  angle  at  one  of  the  vertices  without  setting  up  over  any 
vertex  or  over  any  point  within  the  triangle.  Three  parties  may  work  on 
the  same  triangle,  one  at  each  vertex,  and  the  sum  of  the  three  results  may 
then  be  compared  with  180°  as  a  check. 

Questions:  1.  What  method  can  be  used  when  the  transit  can 
be  set  up  over  a  point  inside  of  the  corner?  2.  How  are  division 
fences  usually  set?  3.  How  are  division  walls  usually  set? 
4.  How  are  fences  along  a  street  usually  set?  5.  How  are 
street  lines  usually  marked? 


3ISES   IN   THE   USE   OF   THE   TRANSIT.       27 

Exercise  T-12. 
Discussion  of  the  Errors  hi  Angular  Measurement. 

Reference:  Chapter  X,  p.  104. 


?:  1.  What  in  general  are  six  sources  of  error  in 
measuring  angles?  p.  104.  2.  What  can  you  say  regarding  the 
relative  importance  of  errors  from  these  different  sources? 
3.  If  the  plumb-bob  is  slightly  off  the  tack  is  the  resulting 
error  likely  to  be  large?  p.  105.  4.  When  is  the  error  due  to 
the  plates  being  out  of  level  likely  to  be  large?  5.  Why  is  the 
error  due  to  either  source  greater  for  short  sights  than  for  long 
sights  in  measuring  angles?  Why  is  the  reverse  true  in  laying  off 
angles?  6.  If  the  bob  is  £  inch  off  the  station,  what,  approxi- 
mately, are  the  resulting  errors  for  sights  of  100  and  1000  feet 
respectively?  7.  Give  some  idea  of  the  errors  involved  when 
one  edge  of  the  limb  is  lower  than  the  other.  8.  In  measuring 
an  angle  what  values  should  be  kept  in  mind  when  judging  the 
importance  of  errors  of  sighting?  (Note  (6),  p.  106.)  9.  What 
values  in  laying  off  angles?  10.  Explain  by  means  of  these 
values  the  importance  of  holding  the  sight  pole  plumb.  11.  Sup- 
pose that  in  measuring  an  angle  to  the  nearest  minute  the  length 
of  sight  is  800  feet  and  only  the  top  of  the  pole  is  visible,  how 
much  could  it  be  out  of  plumb  without  materially  affecting  the 
result?  12.  What  are  some  of  the  natural  sources  of  error? 
13.  Explain  how  the  sun  shining  on  one  side  of  the  instrument 
and  not  on  the  other  might  affect  a  line  of  sight.  14.  Give  some 
precautions  which  may  be  taken  to  avoid  mistakes;  to  eliminate 
constant  errors;  to  eliminate  accidental  errors.  15.  In  what  two 
ways  may  the  precision  of  angular  measurement  be  judged?  p.  107. 
16.  Explain  each  of  these  two  methods.  17.  Explain  the 
fundamental  difference  between  checking  angles  by  the  true  error 
of  their  sum  and  by  the  discrepancy  between  their  sum  and  a 
measured  angle.  18.  If  the  sum  of  the  interior  angles  of  a 
polygon  agrees  with  the  check  of  §  175,  p.  119,  does  this  mean 
that  the  measured  value  of  each  angle  is  exactly  right?  19.  If 
the  interior  angles  of  a  triangle  are  measured  with  a  coarsely 
graduated  instrument  why  is  their  sum  more  likely  to  be 
exactly  180°  than  if  a  finely  graduated  instrument  were  used? 
20.  What  are  some  of  the  conditions  which  effect  the  precision 
of  angular  measurement?  p.  108.  21.  Suppose  that  the  ratio 


28      EXERCISES    IN    THE    USE   OF   THE   TRANSIT. 

of  precision  for  chaining  has  been  fixed  at  Ysl^S)  what  is  the 
permissible  error  for  an  angle?     (See  table  at  bottom  of  p.  108.) 

22.  If  an  error  of  30"  is  made  in  laying  off  an  angle  what  is 
the  error  in  feet  at  a  distance  of   1500  feet  from  the  transit? 

23.  What  can  you  say  regarding  the  permissible  angular  error 
in  ordinary  transit  surveying?  p.  109.     24.    For  limits  j-jj^  or 
higher  what  are  the  permissible  angular  errors,  and  how  may 
this  degree  of  precision  be  attained?     25.    What  is  meant  by 
consistent  accuracy  as  applied  to  the  relation  between  linear  and 
angular  measurement?     26.    When  is  it  not  desirable  to  main- 
tain this  consistent  accuracy?     27.    Suppose  that  contour  points 
in  a  survey  should  be  located  to  the  nearest  foot  and  the  longest 
sight  does  not  exceed  600  feet,  how  accurately  must  angles  be 
read,  and  will  it  be  necessary  to  use  the  vernier?     28.   How 
accurately  must  an  angle  be  measured  to  locate  a  point  800  feet 
from  the  transit  within  \  inch?     29.    A  corner  of  a  building  is 
60  feet  from  a  transit  and  an  angle  and  a  distance  are  measured 
to  it  solely  for  purposes  of  plotting  to  a  scale  of  1  inch  =  50  feet, 
how  accurately  should  each  be  measured?     (Use    500  feet  in 
the  table  at  the  bottom  of  page  108,  changing  the  position  of  the 
decimal  point.)     30.   If  the  permissible  error  in  a  single  angle 
is  20",  what  is  the  permissible  error  in  the  sum  of  the  interior 
angles  of  a  25-sided  polygon?  p.  110.     31.    What  would  be  the 
permissible  error  in    the  same  polygon  if    the  sides  averaged 
400  feet  in  length,  and  the  largest  discrepancy  allowed  between 
two  measurements  of  the  same  line  were  0.1  foot?     32.    Is  it  the 
general    tendency  in    transit    surveying    to    overestimate    the 
accuracy  required  in  angular  measurement  and  underestimate 
that  required  for  linear  measurements,  or  vice  versa? 


GROUP  TB. 

EXERCISES  IN  RUNNING  TRANSIT  LINES. 


General  Directions  for  Exercises  Tr-1  to  Tr-11. 

The  following  eleven  exercises  are  intended  to  fix  in  mind  the 
methods  explained  in  Chapter  XII,  p.  116.  These  exercises  are 
of  the  greatest  importance,  since  they  are  preparatory  to  actual 
surveys  to  be  taken  up  later  in  the  course. 

In  all  problems  drive  three  or  more  stakes  at  random  to  form 
a  triangle  or  polygon,  no  side  of  which  is  less  than  150  feet. 
Mark  each  stake  so  that  different  parties  will  not  use  each  other's 
stations  by  mistake.  It  is  not  necessary  to  drive  stakes  flush  with 
the  ground;  indeed,  it  is  better  to  drive  them  only  partway  in. 
In  the  top  of  each  stake  drive  a  wire  brad,  leaving  enough  of  the 
nail  projecting  above  the  stake  to  serve  as  a  sight,  thus  avoiding 
the  necessity  wherever  possible  of  holding  a  pencil  or  a  pole  on 
the  stake. 

In  the  direct  angle  methods  measure  all  angles  to  the  right, 
unless  otherwise  stated.  Unless  it  is  desirable  to  gain  additional 
practice  in  chaining,  measurements  of  the  lengths  of  the  sides  of 
triangles  or  polygons  may  be  omitted.  In  most  of  the  exercises 
two  men  can  work  to  advantage  in  a  party.  Each  should  check 
the  other's  work,  keep  complete  notes,  and  divide  the  work  of 
running  the  transit.  Thus,  for  example,  if  the  party  consists  of 
two  men,  one  can  run  the  transit  at  one  station,  the  other  at  the 
next  station,  and  so  on,  alternating.  In  the  azimuth  method, 
however,  it  is  desirable  for  one  man  to  run  the  transit  entirely 
around  the  triangle  or  polygon,  and  then  the  exercise  should  be 
repeated,  the  other  man  running  the  transit.  It  is  well  to  choose 
a  comparatively  level  piece  of  ground  for  all  of  these  exercises, 
where  no  difficulty  will  be  encountered  in  sighting. 

Equipment  for  Exercises  Tr-l  to  Tr-11:  A  transit  reading  pref- 
erably to  minutes,  and  for  all  exercises  except  deflection  angle 
exercises,  graduated  according  to  the  full  circle  system.  Also 
hatchet,  stakes,  wire  brads,  crayon,  and  in  some  cases  sight  poles. 
If  the  lengths  of  sides  are  to  be  measured,  a  tape  and  plumb- 
bob  should  be  added  to  the  equipment. 

29 


30         EXERCISES   IN   RUNNING    TRANSIT   LINES. 

Exercise  Tr-1. 

Survey  of  a  Triangle  or  Polygon  by  the  Direct 
Angle  Method. 

References:  Pages  116-120.  §§  162-178. 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29    of  this   book. 

2.  Survey   the   triangle   or   polygon   without    doubling   angles, 
measuring  the  interior  angles.     Keep  notes  according  to  Form  1, 
p.  170.     Follow  as  far  as  possible  the  method  of  procedure  on 
p.  154,  §  220  (a). 

Questions:  1.  Define  transit  station,  transit  line,  and  transit 
angle,  p.  116.  2.  What  are  transit  lines  used  for?  p.  116,  §  165. 

3.  Give  the  general  method  of  running  transit  lines,  p.  116,  §  166. 

4.  Define  transit-line  angle  and  explain  how  to  avoid  ambiguity 
in  the  notes,  p.  117,  §  167.     5.  Define  deflection  angle,  a  system 
of  transit  lines,  traverse,  triangulation.     6.  What  is  the  differ- 
ence between  angles  to  the  right  and  angles  to  the  left?  p.  118. 
7.  If  angles  are  measured  to  the  right,  in  what  direction  must  one 
go  around  a  polygon  in  order  to  measure  interior  angles?  p.  118, 
§  173.     8.  Give  the  rule  for  a  closing  check  on  transit-line  angles. 
9.  If  the  ratio  of   precision  in  chaining  for  a  given  survey  is 
^£<j,  how  accurately  should  transit-line  angles  be  measured  to 
obtain  a  corresponding  degree  of  accuracy  in  angular  measure- 
ment? p.  108,  §  152.     10.  If  the  permissible  error  in  the  meas- 
urement of  a  single  angle  is  30  seconds,  what  is  the  permissible 
error  in  the  sum  of  the  interior  angles  of  a  polygon  of  nine  sides? 
p.  110.    Is  this  error  the  same  thing  as  "error  of  closure  "  ?  p.  119. 

Questions  on  Methods  of  Keeping  Field  Notes  in  Transit  Survey- 
ing: 1.  Describe  the  different  systems  of  keeping  field  notes. 
p.  164,  §§  229  and  231.  2.  How  may  notes  pertaining  to  transit 
lines  be  distinguished  from  other  notes,  and  what  is  the  object 
in  doing  this?  p.  165,  §  230.  3.  Explain  the  tabulated  form  of 
notes.  §  232.  4.  Explain  the  sketch  method.  §  233.  5.  Explain 
the  combination  method.  §  234.  6.  Compare  the  three  methods. 
7.  When  should  notes  read  from  the  bottom  up?  §  235.  8.  What 
should  the  field  notes  include?  §  236.  9.  Give  suggestions  for 
avoiding  crowded  notes.  §  237.  10.  Give  general  suggestions 
for  keeping  field  notes.  §§239  and  240.  11.  Give  the  advantages 
and  disadvantages  of  Form  1,  p.  170. 


EXERCISES   IN    RUNNING   TRANSIT   LINES.         31 

Exercise  Tr-2. 

Measuring  the  Exterior  Angles  of  a  Triangle  or 
Polygon. 

References,  Equipment,  and  Directions,  same  as  for  the  preceding 
exercise,  except  that  exterior  angles  are  measured  instead  of  in- 
terior, by  going  around  the  polygon  in  the  opposite  direction. 


Exercise  Tr-3. 

Doubling  the  Interior  Angles  of  a  Triangle  or 
Polygon. 

Reference:  Page  99,  §  138. 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29  of  this  book. 
2.  Measure  the  interior  angle  of  the  triangle  or  polygon,  doubling 
each  angle  according  to  the  method  on  p.  99,  §  138.  Keep  notes 
according  to  Form  4,  p.  173,  omitting  the  last  two  columns. 
Follow  as  far  as  possible  the  method  of  procedure  on  p.  154, 
§  220  (b). 

Questions:  1.  Explain  the  method  of  measuring  angles  by 
repetition,  p.  99.  2.  Explain  the  use  of  clamps  in  repeating 
the  angles.  Caution,  p.  100.  3.  When  is  it  necessary  to  add 
multiples  of  360°?  §  138  (d).  4.  What  is  the  advantage  of 
doubling  angles?  5.  What  is  the  greatest  number  of  repetitions 
usually  used  for  a  single  angle?  §  138  (c). 


Exercise  Tr-4. 

Doubling  the  Exterior  Angles  of  a  Triangle  or 
Polygon. 

References,  Equipment,  and  Directions,  same  as  for  the  preced- 
ing exercise,  except  that  the  exterior  angles  are  measured  instead 
of  the  interior. 


32         EXERCISES   IN  RUNNING   TRANSIT   LINES. 


Exercise  Tr-5. 

Measuring  the  Interior  Angles  of  a  Triangle  or 

Polygon,  and  Checking  by  Calculated 

Bearings. 

References:  Page  126,  §  189; p.  101,  §  143;  pp.  111-113,  §§  153- 
159;  also  pp.  541-543,  566;  Chapter  XXX,  p.  378. 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29  of  this  book.. 
2.  Set  up  at  any  station,  backsight  on  a  preceding  station,  lower 
the  needle  on  its  pivot,  and  read  the  bearing  of  the  line  to  the 
backsight,  p.  101.  3.  Measure  the  interior  angle  clockwise  and 
check  this  angle  by  the  calculated  bearing  as  in  Chapter  XXX, 
p.  378.  4.  Set  up  at  the  next  station,  measure  the  interior  angle, 
and  from  the  calculated  bearing  of  the  preceding  line  calculate  the 
bearing  of  the  next  line.  Check  this  calculated  bearing  by  read- 
ing the  needle.  5.  Continue  in  the  same  way  until  the  interior 
angle  at  each  station  has  been  measured.  The  discrepancy 
between  the  bearing  of  the  first  line  as  calculated  at  the  last 
station  and  the  magnetic  bearing  of  this  same  line  as  read  at  the 
first  station  should  equal  the  error  in  the  sum  of  the  interior 
angles  as  revealed  by  the  check  on  p.  119. 

Field  Notes:  Keep  notes  according  to  Form  4,  p.  173,  omitting 
of  course  the  double  value  of  the  angle.  Arrange  computations 
of  calculated  bearings  in  a  form  similar  to  that  on  p.  382. 

Suggestion:  Before  beginning  this  exercise  in  the  field,  the  class  should  be 
drilled  in  calculating  bearings;  some  of  the  examples  on  p.  116  of  this  book 
may  be  given  for  practice. 

Questions:  1.  Define  magnetic  declination,  agonic  line,  local 
attraction,  p.  Ill,  §  153.  2.  Define  the  bearing  of  a  line  and 
illustrate  by  a  sketch,  p.  111.  3.  Difference  between  true 
bearing  and  magnetic  bearing?  4.  Why  will  the  true  bearing  of 
a  line  change  if  the  line  is  prolonged  far  enough  with  a  transit? 
5.  Explain  what  is  meant  by  forward  bearing  and  back  bearing 
and  illustrate  by  a  sketch,  p.  112.  6.  If  the  bearing  of  line  A B 
is  N.  47°  W.,  what  is  the  bearing  of  BA?  Note,  p.  113.  7.  Which 
bearings  are  usually  kept  in  a  survey  forward  or  back?  p.  113. 
8.  Give  some  of  the  facts  to  remember  concerning  bearings. 
p.  113.  9.  Which  end  of  the  compass  needle  is  read?  p.  101, 


EXERCISES   IN    RUNNING    TRANSIT    LINES.         33 

§  143.  10.  When  is  the  other  end  read?  p.  102.  11.  Why  are 
positions  of  the  letters  E.  and  W.  interchanged  in  the  compass 
box?  p.  102.  12.  Give  the  directions  to  be  observed  in  reading 
bearings,  p.  103.  13.  Explain  why  the  calculated  bearings  are 
entirely  independent  of  magnetic  bearings,  p.  126,  §  189.  14.  Can 
the  angle  at  any  station  be  checked  by  calculated  bearings  when 
there  is  local  attraction  at  that  station?  Remark,  p.  126. 
15.  Suppose  that  when  an  angle  is  measured  at  the  second  station, 
the  calculated  bearing  and  the  magnetic  bearing  of  the  line  to  the 
third  station  do  not  agree,  and  that  this  discrepancy  continues  at 
succeeding  stations,  what  would  this  indicate?  16.  Is  a  true 
north  and  south  line  ever  used  as  a  basis  for  calculated  bearings? 
Note,  p.  127,  p.  124,  §  185.  17.  What  is  the  check  for  a  closed 
polygon?  p.  127. 

Note:  For  additional  questions  pertaining  to  the  compass,  see  Exercise  Co-2, 
page  70  of  this  book,  and  for  questions  pertaining  to  the  calculation  of 
bearings,  see  page  116  of  this  book. 


Exercise  Tr-6. 

Measuring  the  Interior  Angles  of  a  Triangle  or 
Polygon  to  the  Left. 

References  and  Equipment,  same  as  for  the  preceding  exercise. 

Directions:  Repeat  the  preceding  exercise,  measuring  angles 
to  the  left  instead  of  to  the  right.  Keep  notes  same  as  for  corre- 
sponding exercise,  except  it  should  be  noted  that  all  angles  are 
measured  to  the  left  from  the  backsight.  Keep  magnetic  and 
calculated  bearings. 


Exercise  Tr-7. 

Measuring  the  Exterior  Angles  of  a  Triangle  or 
Polygon  to  the  Left. 

Same  as  the  preceding  exercise,  except  exterior  angles  are 
measured  instead  of  interior. 


34         EXERCISES    IN   RUNNING   TRANSIT    LINES. 


Exercise  Tr-8. 

Measuring  the  Deflection  Angles  of  a  Triangle  or 
Polygon. 

References:  Page  117,  §  168;  page  120,  §  179;  page  155,  §  221. 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29   of  this  book. 

2.  Measure   the   deflection   angles   of  the   triangle   or  polygon 
according  to  the  method  explained  on  page  120.     Keep  notes 
according  to  Form  5,  page  173,  following  as  far  as  possible  the 
method  of  procedure  on  page  155.     Assuming  the  magnetic  bear- 
ing of  the  first  backsight  as  a  basis,  keep  the  calculated  bearings 
as  in  the  preceding  exercises. 

Suggestion:  If  preferred,  stakes  may  be  set  at  random  so  that  the  line 
progresses  more  or  less  in  one  general  direction  instead  of  forming  a  polygon. 

Questions:  1.  What  system  of  numbering  for  the  graduations 
on  the  limb  is  preferable  for  measuring  deflection  angles?  p.  75, 
§  96  (c) ;  also  Remark,  bottom  of  p.  73.  2.  Give  a  valuable 
check  used  in  the  deflection  angle  method,  p.  155,  §  221  (b). 

3.  If  it  were  desired  to  double  deflection  angles,  how  would  you 
proceed?  p.  100,  §  138  (e).     4.  What  error  is  thus  eliminated? 
5.  What  check  may  be  used  when  calculated  bearings  are  kept? 
Bottom  of  page  155.     6.  Explain  how  setting  the  B  vernier  at 
the  original  deflection  angle  gives  a  double  check.     Step  8,  p.  155. 
7.  Explain  two  forms  for  keeping  notes  for  deflection  angles  and 
the  advantages  and  disadvantages  of  each.  pp.  173,  174. 


Exercise  Tr-9. 

Survey  of  a  Triangle  or  Polygon  by  the  First 
Azimuth  Method. 

References:  Pages  114,  115;  p.  120,  §  180  (a),  (b),  (c);  also 
p.  156,  §  222. 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29  of  this  book. 
2.  Survey  the  triangle  or  polygon  by  the  first  azimuth  method, 


EXERCISES   IN   RUNNING   TRANSIT   LINES.         35 

p.  121,  going  around  the  triangle  clockwise.  Assume  a  magnetic 
north  and  south  line  for  a  meridian.  Keep  notes  according  to 
Form  7,  p.  174.  Check  all  azimuths  by  magnetic  bearings. 

Suggestion:  If  the  party  consists  of  two  men,  one  should  run  the  transit 
until  the  exercise  is  completed,  and  then  the  work  may  be  repeated,  the  other 
man  running  the  transit  and  going  around  the  triangle  or  polygon  in  the 
opposite  direction. 

Questions:  1.  Define  the  azimuth  of  a  line.  p.  114.  2.  Why 
do  many  surveyors  measure  azimuths  from  the  south  as  a  starting- 
point  instead  of  the  north?  3.  What  is  the  chief  advantage  in 
measuring  azimuths  from  the  north?  4.  Is  the  azimuth  always 
measured  from  a  north  and  south  line  as  a  reference  line?  §  160(c). 
b.  Explain  the  difference  between  forward  azimuth  and  back 
azimuth.  6.  Compare  the  method  of  measuring  azimuths  with 
the  method  of  measuring  bearings,  p.  115,  §161.  7.  Give 
additional  facts  to  remember  about  azimuths.  §  161.  8.  By 
means  of  a  sketch  explain  the  first  method  of  running  transit 
lines  by  azimuths,  p.  121.  9.  What  precautions  should  be 
taken  in  beginning  a  survey  by  azimuths?  p.  123,  §  182.  10.  How 
may  azimuths  be  checked  by  the  magnetic  needle?  p.  124,  §  184. 

11.  If  at  any  station  the  azimuth  and  bearing  of  a  line  disagree, 
does  it  necessarily  follow  that  the  former  is  incorrect?  p.  123,  §182. 

12.  What  other  meridians  are  used  besides  the  magnetic  north 
and  south  line?  p.  124,  §§  185,  186.    13.  If  a  true  north  and  south 
line  is  used  as  a  reference  meridian,  how  should  the  compass  be 
adjusted?     14.  What   is   the   advantage   of   such   a   meridian? 
15.  What  is  the  disadvantage  of  using  a  line  assumed  at  random 
as  a  reference  meridian?  §  186.     16.  What  is  meant  by  orienting 
the  transit?  p.  125.     17.  In  step  5,  p.  156,  how  does  setting  the 
vernier  at  the  forward  azimuth  act  as  a  check?     If  the  line  of 
sight  does  not  exactly  strike  the  foresight,  what  should  be  done? 


36        EXERCISES   IN   BUNKING  TRANSIT   LINES. 


Exercise  Tr-10. 

Survey  of  a  Triangle  or  Polygon  by  the  Second 
Azimuth  Method. 

References:  Page  122,  §  180  (d),  §§  181, 183 ;  also  p.  156,  §  222  (b) 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29  of  this  book. 
2.  Proceed  as  in  the  preceding  exercise,  but  use  the  second 
azimuth  method  instead  of  the  first. 

Questions:  1.  By  means  of  a  sketch  explain  the  second  azimuth 
method,  p.  122.  2.  Compare  step  by  step  the  two  azimuth 
methods.  §  181.  3.  Give  the  advantages  and  disadvantages  of 
each  of  the  two  azimuth  methods.  §  183. 

Note:  If  time  permits,  repeat  this  problem  but  go  around  the  triangle  or 
polygon  counter-clockwise. 


Exercise  Tr-11. 

Survey  of  a  Triangle  or  Polygon  by  the  Method 
of  Bearings. 

References:  Page  125,  §  188;  also  p.  156,  §  222  (d). 

Equipment:  See  page  29  of  this  book. 

Directions:  1.  See  general  directions,  page  29  of  this  book. 
2.  Assume  either  a  true  north  and  south  line  or  a  magnetic  north 
and  south  line  as  a  reference  meridian,  and  proceed  exactly  as 
directed  in  Exercise  Tr-9,  but  use  the  method  of  bearings  as 
explained  on  page  125  instead  of  the  method  of  azimuths. 

Questions:  1.  Explain  by  a  sketch  the  method  of  running 
transit  lines  by  bearings.  2.  Which  of  two  zeroes  on  the  limb 
should  be  called  the  north  zero,  and  why,  in  most  cases,  would 
this  zero  really  be  nearer  the  south  end  of  a  telescope  pointed 
north?  Note,  bottom  of  p.  125.  3.  What  is  a  common  mistake 
in  this  method?  Caution,  p.  126.  4.  What  precautions  should 
be  taken  in  starting  the  survey?  Note,  p.  126. 

Note:  As  this  method  of  bearings  is  not  commonly  used,  it  may  be  well 
to  omit  the  field  work  in  this  exercise,  simply  discussing  the  above  questions 
in  class. 


EXERCISES  IN   RUNNING   TRANSIT   LINES.         37 


Exercise  Tr-13. 

Questions  on  the  Methods  of  Running  Transit  Lines 
or  Traverses. 

Reference:  Pages  127-131. 

Questions:  1.  Give  the  advantages  and  disadvantages  of  the 
direct  angle  method,  p.  127.  2.  Give  the  method  of  procedure 
for  the  direct  angle  method  at  any  one  station,  (a)  when 
angles  are  not  doubled;  (b)  when  angles  are  doubled,  p.  154. 
3.  Give  the  advantages  and  disadvantages  of  the  deflection 
angle  method,  p.  128.  4.  Give  the  method  of  procedure  for 
the  deflection  angle  method,  p.  155.  5.  Give  the  advantages 
and  disadvantages  of  the  azimuth  method,  p.  128.  6.  Give 
the  method  of  procedure  for  the  azimuth  method,  p.  156. 
7.  Give  the  advantages  and  disadvantages  of  the  method  of 
bearings,  p.  129.  8.  Give  the  advantages  and  disadvantages 
of  the  method  of  calculated  bearings,  p.  129.  9.  Give  the 
advantages  and  disadvantages  of  the  method  of  measuring 
angles  by  repetition,  p.  130.  10.  For  what  purposes  are  transit 
lines  used?  p.  130.  11.  Does  a  system  of  transit  lines  neces- 
sarily close?  p.  130.  12.  Does  it  make  any  difference  whether 
the  exterior  or  interior  angles  of  the  polygon  are  measured? 
p.  130.  13.  What  is  the  check  for  the  sum  of  the  interior 
angles  of  a  polygon?  p.  119.  14.  What  is  meant  by  the  error 
of  closure?  To  what  is  it  due?  p.  119.  15.  Name  four  meth- 
ods of  running  transit  lines.  16.  What  is  the  principal  differ- 
ence between  the  direct  angle  and  the  deflection  angle  methods? 
17.  What  are  the  three  different  kinds  of  meridians  used  in 
the  azimuth  method?  When  would  you  use  one  and  when  the 
other?  p.  130.  18.  Give  two  methods  of  orienting  the  transit 
in  the  azimuth  method,  p.  131.  19.  What  does  a  discrep- 
ancy between  the  azimuth  and  the  magnetic  bearing  of  a  line 
indicate?  p.  131.  20.  What  is  the  purpose  of  keeping  calcu- 
lated bearings,  and  when  would  you  use  this  method?  p.  131. 

21.  Name  some  of  the  places  where  any  method  of  checking 
foresight  lines  by  the  magnetic  needle  would  be  useless,  p.  131. 

22.  When  would  you  use  the  method  of  doubling  angles?  p.  13] . 


GROUP  Ts. 

TRANSIT  SURVEYS. 

The  first  three  exercises  in  this  group  are  intended  for  class-room  discussion, 
the  object  being  to  help  the  student  to  gain  a  working  knowledge  of  the 
general  methods  used  in  making  an  ordinary  transit  survey.  He  will  then 
be  better  prepared  to  undertake  the  actual  surveys  suggested  in  the  last 
exercise  of  this  group. 

Exercise  Ts-1. 
Discussion  of  the  Methods  of  Locating  Details. 

(For  questions  on  the  methods  of  locating  details  by  linear  measurements 
only,  see  page  15  of  this  book.) 

1.  Give  the  general  method  of  locating  objects  from  transit 
lines,  p.  133.  2.  Are  all  parts  of  the  same  object  always 
located  from  one  transit  station?  p.  133.  3.  Give  a  common 
method  of  locating  objects  by  angles  and  distances,  p.  134, 
§  195  (a).  4.  Give  the  corresponding  method  for  azimuths  and 
distances.  5.  Give  the  method  of  locating  a  building  by  pro- 
longing one  side  until  it  intersects  the  transit  line.  p.  135. 

6.  Give  a  method  for  locating  large  or  irregular  curves,  p.  135. 

7.  Give  the  method  of  locating  a  point  by  an  angle  and  a  dis- 
tance, when  the  distance  is  measured  from  some  fixed  point 
other  than  the  transit  station.     Illustrate  by  the  location  of  a 
building,  p.  136,  §  195  (d).     8.   How  is  the  method  of  the  pre- 
ceding question  used  for  determining  the  direction  of  a  street 
line?  §  195  (e).     9.    Explain  the  method  of  locating  an  irregular 
line,  as,  for  example,  the  bank  of  a  stream,  by  a  base  line  and 
two  intersecting  angles,  p.  137,  §  196.     10.    Give  some  practical 
suggestions  for  locating  points  on  the  water  by  the  method  of 
the  preceding  question,  i.e.  methods  of  taking  angles,  of  keeping 
notes  and  of  giving  signals,  p.  203,  §  261.     11.    Give  the  three- 
point   method  of   locating   points  on   the   water,  p.  137,  §  197. 

12.  Give    four    methods    of    locating    boundary    lines,  p.  141. 

13.  Give   the   advantages   and   disadvantages   of  the  different 
methods  of   the  preceding  question,  pp.  141,   142;    also   §  216. 

14.  What    are    the    two    most    common    methods    of    locating 
details?  p.  156,  §  223. 

Note:  The  above  questions  should  be  supplemented  by  a  careful  discus- 
sion of  the  methods  used  for  locating  details  in  the  various  surveys  illustrated 
on  pages  176  to  190.  (See  Questions  22  to  28  of  the  next  exercise.)  Study 
with  special  care  Illustration  V,  p.  184,  as  it  shows  a  large  variety  of  methods 
of  locating  details. 


TRANSIT    SURVEYS.  39 

Exercise  Ts-2. 
Discussion  of  the  Methods  of  Keeping  Field  Notes. 

Reference:  Chapter  XV,  page  164. 

Questions:  1.  What  can  you  say  regarding  the  different 
methods  of  keeping  field  notes?  p.  164.  2.  Why  should  notes 
pertaining  to  transit  lines  be  distinguished  from  all  other  notes? 
p.  165.  3.  Give  several  methods  of  accomplishing  this  result. 

4.  Explain   the   three   general   forms   used    in   keeping   notes? 

5.  When    can    the    tabulated    form    be    used     to     advantage? 

6.  What  are  the  advantages  and  disadvantages  of  the  sketch 
method?     7.    Give  suggestions  for  keeping  notes  by  the  com- 
bination  method,   p.    166.     8.    When  should   notes   read   from 
the  bottom  of  the  page  upward?     9.    What  two  kinds  of  data 
should  field  notes  include?  p.    167.     10.    Give  suggestions  for 
avoiding  crowded  notes.     11.    How  are  several  pages  of  notes 
made  continuous?     12.    Give  suggestions  for  a  general  sketch  of 
transit  lines,   p.    168.     13.    What  must  be  made  clear  in  the 
notes    regarding    any    linear    measurement?     Regarding    any 
angle?     14.    What  is  the  difference  between  entering  an  angle 
in  the  notes  as  ABC  and  CBA?     (See  Note,  p.  90.)     15.    What 
else   must   be  understood   to   make   a   notation   such  as   ABC 
perfectly   definite?   p.    117.     16.    What   should   be   a   constant 
thought  in  keeping  notes?     Suggestions,  p.  169.     17.    What  are 
the  advantages  of  Form  1,  p.  170?     Disadvantages?     18.    Inter- 
pret the  notes  on  p.  172;  give  the  advantage  and  disadvantages 
of  this  form.     19.    Interpret  Form  4,  p.  173.     What  unnecessary 
check  seems  to  have  been  employed,  judging  from  the  notes  as 
they  stand?     (See  Comments,  p.   154.)     20.    Interpret  Form  5, 
p.   173;  give  the  advantages  and  disadvantages  of  this  form; 
compare  it  with  Form  6,  p.  174.     21.    Interpret  form  7,  p.  174. 
22.    Describe  how  the  survey  on  page  177  was  made,  explaining 
how  the  notes  for  each  step  were  recorded.     23.    Describe  how 
the  survey  on  page  179  was  made,  and  comment  upon  the  notes. 
24.    Describe  how  the  survey  shown  on  the  insert  sheet  opposite 
page   190  was  made.     Comment  upon  special  features  of  the 
notes,  p.  181.     25.   Describe  the  survey  on  p.  183  and  comment 
upon  the  notes.     26.  Interpret  the  notes  of  Illustration  V  on  the 
insert  sheet  opposite  p.  190,  explaining  carefully  how  each  point 
was  located.     27.    Interpret  the  notes  on  p.  187.    28.    Interpret 
the  notes  on  p.  189,  and  explain  important  steps  in  the  survey. 


40  TRANSIT    SURVEYS. 


Exercise  Ts-3. 

Discussion  of  Practical  Questions  of  Field  Work  in 
Transit  Surveying. 

1.  Describe  the  signals  commonly  used  in  field  work.  p.  146. 
2.  Give  the  general  method  of  making  a  transit  survey,  p.  146; 
p.  132,  §§  192,  193.  3.  Give  different  methods  of  establishing 
a  transit  station.  §  207.  4.  Give  methods  of  marking  guard 
stakes.  5.  Give  suggestions  for  numbering  or  lettering  stations. 
p.  147.  6.  Give  suggestions  for  choosing  a  place  for  a  transit 
station,  p.  148.  7.  Give  methods  of  referencing  a  station, 
p.  148,  p.  54,  p.  203.  8.  What  is  the  first  consideration  gov- 
erning field  work?  p.  149,  §  214.  9.  What  relation  between  field 
work  and  office  work  should  be  kept  in  mind?  p.  149.  10.  Give 
suggestions  for  determining  where  to  run  transit  lines,  p.  149. 
11.  Illustrate  the  preceding  question  by  different  methods  of 
making  a  boundary  survey,  compare  the  different  methods, 
and  show  how  the  field  work  and  office  work  may  be  affected 
by  the  choice  of  stations,  p.  150.  12.  What  method  of  running 
transit  lines  would  you  use  for  city  work?  what  method  for 
country  surveying?  for  stadia  and  topographic  surveying? 
p.  151.  13.  In  what  kind  of  work  is  the  deflection  angle 
method  used?  p.  151.  14.  Are  different  methods  ever  com- 
bined in  the  same  survey?  p.  151.  15.  Give  suggestions  for 
running  transit  lines  with  reference  to  precautions  taken  and 
checks  used.  p.  152.  16.  What  are  some  of  the  precautions 
and  checks  involved  in  any  systematic  method  of  procedure? 
p.  153.  17.  Why  should  some  systematic  method  of  procedure 
be  followed?  Remark,  p.  154.  18.  Give  the  method  of  pro- 
cedure for  the  direct  angle  method  when  angles  are  not  doubled ; 
when  angles  are  doubled,  p.  154.  19.  Give  the  method  of 
procedure  for  the  deflection  angle  method,  p.  155.  20.  Give 
the  method  of  procedure  for  the  azimuth  method,  p.  155. 
21.  When  several  methods  of  locating  a  detail  may  be  em- 
ployed, give  some  of  the  considerations  which  would  influence 
you  in  the  choice  of  .method,  p.  156.  22.  Give  suggestions  for 
selecting  points  of  an  object  to  be  located,  p.  157.  23.  In 
filling  in  the  details  of  a  survey,  should  all  measurements  be 
taken  with  equal  accuracy?  p.  157.  24.  Give  suggestions  for 
locating  street  lines,  p.  158.  25.  In  locating  buildings,  what  is 


THAN  SIT    SURVEYS.  41 

always  necessary  to  complete  the  work?  Practical  suggestions, 
p.  158.  26.  Should  the  lengths  of  boundary  lines  be  meas- 
ured? 27.  If  the  corner  of  a  building  is  100  feet  from  the 
transit,  and  the  map  is  to  be  plotted  to  the  scale  of  one  inch 
equals  50  feet,  how  close  should  the  angle  to  a  corner  be  read 
for  the  purpose  of  locating  the  corner  by  angle  and  distance? 
See  Question,  p.  158;  also  p.  105,  §  147.  28.  Give  some  general 
suggestions  for  staking  out  work.  p.  158.  29.  Discuss  the 
different  methods  of  keeping  field  notes,  pp.  164,  165,  166. 

30.  Give  general  suggestions  for  keeping  field  notes,  pp.  167-169. 

31.  Summarize  the  important  points  brought  out  in  the  dis- 
cussion of  errors,  p.  159,  §  226.     32.   What  are  the  permissible 
errors  of  closure  for  different  classes  of  work?   p.  160,  §  227. 
33.    Discuss  the  duties  of  the  different  members  of  a  transit 
party,  p.  161. 


Exercise  Ts-4. 
Transit  Survey  of  a  Small  Area. 

Reference:  Chapter  XIV,  p.  145. 

Equipment:  See  Art.  204,  p.  145.  If  the  party  consists  of 
four  men  the  chainmen  should  divide  between  them  the  equip- 
ment of  the  axeman  and  flagman. 

Directions:  Make  a  survey  of  a  small  tract  of  land,  locating  all 
important  features  such  as  boundaries,  buildings,  and  fences. 
Use  the  direct  angle  method  of  running  transit  lines;  double 
all  transit  line  angles,  but  do  not  double  angles  in  locating 
details.  Follow  carefully  the  method  of  procedure  given  in 
Article  220  (6),  page  154. 

Note:  At  the  beginning  of  this  exercise  it  is  well  for  the  instructor  to 
take  each  party  over  the  tract  to  be  surveyed,  discussing  where  to  run  the 
transit  lines  (p.  149),  and  choosing,  tentatively,  places  for  transit  stations 
(p.  148),  It  should  be  clearly  understood  what  details  are  to  be  located, 
though  the  choice  of  method  for  locating  each  point  may  be  left  to  the 
student.  Methods  of  marking  guard  stakes,  of  keeping  notes,  of  locating 
details  and  other  questions  pertaining  to  field  work  suggested  in  the  three 
preceding  exercises  should  be  discussed  thoroughly  before  beginning  this 
exercise. 

Exercises  similar  to  this  but  involving  different  methods  of  running  transit 
lines  should  be  given  also.  It  is  better  to  make  several  small  surveys  by 
different  methods  than  to  make  one  large  survey  in  which  only  one  method 
of  running  transit  lines  is  used. 


GROUP  TP. 

SPECIAL  PROBLEMS  IN  TRANSIT  SURVEYING. 

The  first  seven  exercises  in  this  group  are  illustrations  of  geometrical  and 
trigonometrical  problems  which  occasionally  arise  in  transit  surveying,  but 
which  are  of  too  infrequent  occurrence  to  be  considered  apart  of  routine 
field  work.  The  remaining  three  exercises  are  special  problems  in  staking 
out  work. 

Exercise  Tp-1. 
Practice  in  Triangulation. 

Reference:  Chapter  XVI,  page  191. 

Equipment:   Transit,  reading  preferably  to  30  or  20  seconds. 

Directions:  1.  Establish  several  tripod  signals  similar  to  that 
described  on  page  198,  §  252.  This  should  be  done  once  for  all 
by  the  whole  class.  2.  Measure  the  angles  at  each  station 
according  to  the  method  described  in  §  250.  Keep  notes 
according  to  form  on  p.  197. 

Suggestions:  Each  man  in  the  squad  should  measure  as  many  angles  as 
time  permits,  using  different  transits  if  practicable.  Limits  of  error  should 
be  established  by  the  instructor.  See  p.  199,  §  253.  If  desired,  a  base 
line  may  be  laid  out  and  a  regular  network  of  triangles  established, 
although  it  is  probably  better  to  leave  this  until  a  regular  survey  is  made, 
as  the  main  object  of  this  exercise  is  to  accustom  the  student  to  the  method 
of  measuring  angles. 

Questions:  1.  What  is  meant  by  triangulation  and  a  net- 
work or  system  of  triangles?  p.  191.  2.  When  would  triangu- 
lation be  employed?  §  244  (a).  3.  How  large  an  area  may  be 
covered  by  triangulation  in  plane  surveying?  p.  191,  §  244. 

4.  Give  some  of  the  sources  of  error  in  triangulation.  p.  191. 

5.  Give  some  of  the  things  to  be  considered  in  the  choice  of 
stations,  p.  192.     6.   What  are  some  of  the  things  to  be  con- 
sidered in  choosing  a  place  for  a  base  line?  p.  193.     7.    If  the 
base  line  is  laid  off  on  a  railroad  track,  how  may  the  ends  of  the 
base  be  transferred  to  points  not  on  the  railroad?     Bottom  of 
p.  193.     8.    When  are  new  or  additional  base  lines  introduced 
in  an  extensive  survey?     9.   What  considerations  govern  the 
length  of  the  base  line?  p.  194.     10.    Give  different  methods  of 
measuring  a  base  line.  p.  194.     11.    If  it  is  impossible  to  estab- 
lish a  single  line  of  sufficient  length  for  a  base  line,  how  would 

42 


SPECIAL   PROBLEMS    IN    TRANSIT    SURVEYING.     43 

you  proceed?  Remark,  p.  193.  12.  What  angles  are  measured 
in  triangulation?  p.  194.  13.  Give  the  sources  of  error  which 
should  be  eliminated  in  the  measurement  of  angles,  p.  194, 
§  250.  14.  Give  a  method  of  procedure  involving  the  method 
of  repetition,  p.  195.  15.  Give  some  practical  suggestions  for 
measuring  angles,  p.  196.  16.  Give  suggestions  for  keeping 
field  notes  for  triangulation.  p.  198.  17.  Give  some  practical 
suggestions  for  constructing  signals,  p.  198.  18.  What  should 
be  the  diameter  of  the  mast?  p.  199.  19.  What  errors  are 
allowable  in  centering  a  mast  over  a  station?  p.  199.  20.  What 
is  meant  by  the  eccentricity  of  a  station?  Give  an  illustration, 
p.  199.  21.  Give  examples  of  the  accuracy  attained  in  actual 
practice,  p.  199,  §  253.  22.  How  may  trigonometric  leveling  be 
combined  with  triangulation?  p.  200. 


Exercise  Tp-2. 
To  Prolong  a  Straight  Line  through  an  Obstacle. 

References:  Page  219,  §§  276,  277. 

Equipment:  Transit,  steel  tape,  stakes,  hatchet,  sight  poles, 
and  chain  pins. 

Directions:  1.  Drive  two  stakes,  A  and  B,  from  150  to  200 
feet  apart.  2.  Prolong  this  line  through  an  imaginary  obstacle 
by  the  second  method  of  §  277  (a),  p.  220.  3.  Check  by  the 
third  method.  4.  After  the  work  has  been  checked  by  the 
third  method,  sight  along  the  line  through  the  imaginary 
obstacle  as  an  additional  check. 

Field  Notes:  Make  a  complete  sketch  showing  all  angles  and 
distances  measured  or  laid  off.  Show  the  error  made  in 
alignment. 

Suggestion:  For  class  work  an  imaginary  obstacle  is  better  than  a  real 
obstacle,  as  it  permits  the  check  of  step  (4)  above.  If  time  permits,  how- 
ever, it  is  well  to  repeat  the  problem,  running  a  line  through  a  real  obstacle 
instead  of  an  imaginary  one. 

Questions:  1.  When  is  the  rectangle  method  of  Fig.  277  (a)  a 
satisfactory  one  to  use?  2.  How  can  short  backsights  be 
avoided  in  the  rectangle  method?  3.  What  is  the  advantage 
of  the  equilateral-triangle  method  as  compared  with  the  third 


44   SPECIAL,  PROBLEMS   IN   TRANSIT   SURVEYING. 

method  of  §  277?  4.  What  is  the  sole  advantage  of  the  third 
method?  5.  Give  practical  suggestions  for  laying  off  the 
angles. 

Note:  Problems  Tp-2  to  Tp-6  are  special  cases  of  triangulation,  and  if 
great  accuracy  were  required  refined  methods  of  measuring  base  lines  and 
angles  would  be  employed.  It  is  sufficient,  however,  for  class  work,  to 
dispense  with  this,  using  only  such  precautions  as  are  taken  in  ordinary 
transit  surveying. 

Exercise  Tp-3. 

To  Run  a  Line  between  Two  Given  Points  when 
an  Obstacle  Intervenes. 

Reference:  Page  221,  §  277  (b). 

Equipment:  Transit,  tape,  hatchet,  stakes,  and  sight  poles. 

Directions:  1.  Drive  two  stakes  A  and  B  from  200  to  300 
feet  apart.  2.  Imagine  an  obstacle  about  half  way  between 
them,  and  run  a  line  from  A  to  B  by  the  first  method  of  Fig. 
277  (b).  3.  Check  by  the  second  method  of  Fig.  277  (b). 
4.  Sight  from  A  to  B  as  a  final  check. 

Field  Notes  and  Suggestions:  See  preceding  problem. 

Questions:  1.  Draw  a  sketch  illustrating  a  third  method. 
Compare  the  two  methods  of  Fig.  277  (b). 


Exercise  Tp-4. 

To  Measure  between  Two  Points  when  One  is 
Inaccessible. 

Reference:  Page  222,  §  277  (c). 

Equipment:  Transit,  steel  tape,  hatchet,  stakes,  sight  pole, 
and  chain  pins. 

Directions:  1.  Drive  two  stakes  A  and  B  from  200  to  300 
feet  apart,  and  assume  B  to  be  inaccessible.  2.  Find  the 
distance  from  A  to  B  by  the  first  method,  Fig.  277  (c).  3. 
Check  the  distance  AB  by  the  second  method.  4.  Measure  the 
distance  AB  with  the  tape  as  an  additional  check. 

Field  Notes:  1.  Make  a  sketch  showing  all  angles  and  dis- 
tances measured  or  laid  off.  2.  Arrange  computations  system- 
atically, and  give  the  discrepancy  between  the  lengths  of  AB 


SPECIAL   PROBLEMS   IN   TRANSIT    SURVEYING.      45 

as  found  in  steps  (2)  and  (3)  and  its  length  as  found  by  meas- 
urement with  the  tape. 

Questions:  1.  Compare  the  first  and  second  method.  2.  Give 
a  third  method  that  may  be  used  when  both  ends  of  the  line  are 
accessible.  3.  How  may  each  of  the  three  methods  be  checked 
without  resorting  to  a  different  method?  4.  Explain  by  means 
of  a  sketch  how  to  measure  the  distance  between  two  given 
points  when  one  is  invisible  from  the  other  and  is  also  inacces- 
sible, p.  223. 

Exercise  Tp-5. 

To  Measure  between  Two  Points  when  Both  are 
Inaccessible. 

Reference:  Page  223,  §  277  (e). 

Equipment:  Transit,  steel  tape,  stakes,  hatchet,  chain  pins, 
and  sight  pole. 

Directions:  1.  Drive  two  stakes,  A  and  B,  from  200  to  400 
feet  apart,  and  assume  both  points  to  be  inaccessible.  2.  Lay 
off  a  convenient  base  line  CD,  and  find  by  triangulation  the 
distance  AB  as  explained  in  §  277  (e).  3.  Measure  the  dis- 
tance A  B  with  a  tape  as  a  check. 

Field  Notes:  1.  A  complete  sketch  showing  all  distances  and 
angles  measured  or  laid  off.  2.  A  systematic  arrangement  of 
all  computations.  3.  Give  the  discrepancy  between  the  com- 
puted length  of  A  B  and  its  length  as  measured  with  the  tape. 

Suggestions:  In  this  problem  it  is  well  to  measure  the  angles  and  the 
triangles  by  the  method  of  repetition.  Doubling  the  angles  will  be  suffi- 
cient unless  the  base  line  is  measured  with  great  accuracy,  when  the  method 
on  p.  195  may  be  employed. 

Exercise  Tp-6. 

To  Measure  the  Height  of  an  Inaccessible  Point. 

Reference:    Page  223,  §  277  (f). 

Equipment:  Transit,  steel  tape,  hatchet,  stakes,  chain  pins, 
and  sight  pole. 

Directions:  1.  Find  the  height  of  some  inaccessible  point  as 
the  top  of  a  flag  pole,  a  point  on  a  high  building,  or  some  other 
definite  point,  by  the  method  explained  in  §  277  (f).  The  ele- 


46      SPECIAL   PROBLEMS    IN    TRANSIT    SURVEYING. 

vation  of  the  inaccessible  point  should  be  determined  with 
reference  to  some  definite  point  or  bench  mark  near  the  ground. 
2.  Repeat  the  problem  as  a  check,  using  a  different  base  line. 

Field  Notes:  A  sketch  showing  all  angles  and  distances  meas- 
ured. A  systematic  arrangement  of  all  computations.  Give 
the  discrepancy  between  the  first  and  second  results. 

Suggestion:  If  desired,  two  or  more  parties  may  work  simultaneously 
determining  the  elevation  of  the  same  inaccessible  point,  and  thus  save 
the  time  required  for  repeating  the  exercise  as  a  check. 

Note:  Notice  that  the  height  required  is  measured  from  a  point  on  the 
ground  and  not  from  the  supporting  axis  of  the  telescope.  This  involves 
rinding  the  height  of  the  supporting  axis  with  respect  to  the  point  on  the 
ground,  and  this  may  be  found  either  by  the  vertical  angle  method,  or,  if 
preferred,  by  the  use  of  the  leveling  rod. 

Exercise  Tp-7. 
Perpendiculars  and  Parallels. 

(Exercise  for  the  blackboard  and  notebook.) 

Reference:  Page  224,  §  278. 

Directions:  Explain  by  means  of  sketches  the  following 
methods : 

1.  To  establish  a  perpendicular  to  a  given  line  from  any 
given  point;  (a)  when  the  given  line  and  the  given  point  are 
both  accessible;  (b)  when  the  given  line  is  accessible,  but  the 
given  point  is  inaccessible;  (c)  when  the  given  point  is  acces- 
sible, but  the  given  line  is  inaccessible.  2.  To  establish  a  line 
through  a  given  point  parallel  to  a  given  line;  (a)  when  the 
given  line  and  the  given  point  are  both  accessible;  (b)  when 
the  given  line  is  accessible,  but  the  given  point  is  inaccessible; 
(c)  when  the  given  point  is  accessible,  but  the  given  line  is 
inaccessible. 

Exercise  Tp-8. 
To  Stake  Out  a  Building. 

References:  Page  209,  §  266;  also  p.  158,  §  224. 

Equipment:  Transit,  tape,  hatchet,  stakes,  sight  pole. 

Directions:  1.  Drive  two  stakes  A  and  B  from  300  to  400  feet 
apart.  Let  these  represent  merestones  which  determine  a 
street  line.  2.  Set  stakes  for  the  house  whose  dimensions  are 
given  on  p.  183,  making  the  front  of  the  house  parallel  to  and 


SPECIAL   PROBLEMS    IN    TRANSIT    SURVEYING.      47 

30  feet  from  the  street  line  AB  and  at  some  fixed  distance  from 
A  measured  along  the  street  line. 

Field  Notes:  Make  a  complete  sketch  similar  to  that  on 
p.  210,  showing  all  measurements  made,  dimensions  of  the 
house  and  the  location  of  reference  points;  indicate  also  all 
points  where  the  transit  is  set  up.  Give  the  discrepancy,  if  any, 
between  the  lengths  of  the  diagonals  of  the  reference  rectangle. 

Suggestions:  1.  As  it  is  usually  impracticable  in  class  work  to  actually 
set  batter-boards,  a  stake  should  be  driven  wherever  a  point  would  be 
fixed  on  a  batter-board.  2.  Before  beginning  the  problem,  the  student 
should  make  a  rough  sketch  and  plan  the  work  so  that  it  may  be  done  in 
the  shortest  time  without  sacrificing  accuracy. 

Questions:  1.  Give  some  general  suggestions  for  staking  out 
work.  p.  158,  §  224.  2.  What  is  the  usual  method  of  setting 
batter-boards,  and  at  what  elevation?  p.  208,  §§  265,  266.  3. 
Assuming  that  the  top  of  a  foundation  will  be  wholly  below  the 
existing  surface  of  the  ground  so  that  when  the  building  is  first 
staked  out  it  is  impossible  to  set  the  batter-boards  at  the  proper 
elevation,  how  would  you  proceed?  4.  Give  the  general  method 
of  staking  out  a  building,  p.  209.  5.  Sketch  another  method 
which  is  as  good  as,  or  better  than,  the  one  used  for  staking  out 
the  house  on  p.  210.  6.  Where  should  reference  points  be 
placed?  §  266  (b).  7.  Give  at  least  two  or  three  different 
methods  for  staking  out  a  building  whose  front  is  on  line  with 
an  existing  building. 

Questions  on  Staking  Out  a  House  Lot,  a  Highway,  a  Retaining- 
wall,  an  Abutment,  and  a  Tunnel:  1.  Give  the  general  method  of 
staking  out  a  house  lot.  p.  210.  2.  Give  different  methods  of 
marking  the  corners  of  the  boundaries,  p.  211.  3.  Give  the 
general  method  for  staking  out  a  highway,  together  with  some 
practical  suggestions,  p.  212.  4.  Explain  the  general  method 
of  giving  lines  for  a  retaining-wall.  p.  213.  5.  Which  lines  of 
a  retaining-wall  are  usually  staked  out?  6.  How  are  lines 
given  for  an  excavation?  p.  213.  7.  When  retaining-walls  are 
built  in  sections,  how  may  they  be  staked  out?  p.  213.  8.  When 
walls  are  on  a  curve,  how  are  stakes  set?  p.  214.  9.  Illustrate 
by  a  sketch  how  you  would  set  stakes  for  a  wing  abutment. 
10.  How  would  you  proceed  in  the  preceding  question  if  the 
face  of  the  abutment  is  in  the  water  where  the  transit  cannot 
be  set  up?  11.  Explain  the  general  method  of  giving  the  line 
for  a  tunnel.  12.  When  the  preliminary  straight  line  between 


48     SPECIAL   PROBLEMS    IN   TRANSIT   SURVEYING. 

the  ends  of  a  tunnel  cannot  be  run  because  of  obstacles,  how 
would  you  proceed? 

Note:    If    time    permits,  additional    exercises    suggested    by  the    above 
questions  may  be  given  in  staking  out  work. 


Exercise  Tp-9. 
To  Locate  Piers  for  a  Bridge. 

References:  Page  215,  §  275,  and  Chapter  XVI,  p.  191. 

Equipment:  Transit,  tape,  spring  balance,  thermometer,  ax, 
stakes,  leveling  rod,  sight  poles. 

Directions:  1.  Assume  two  points  A  and  B  from  400  to  600 
feet  apart;  let  these  points  determine  the  axis  of  the  bridge. 
2.  Lay  off  base  lines  of  suitable  lengths  at  A  and  B.  3.  Find 
the  distance  from  A  to  B,  and  locate  a  pier  half-way  between 
them  according  to  the  method  explained  in  §  275  (b)  and  (c). 
4.  After  the  center  of  the  pier  has  been  established,  not  before, 
measure  the  distances  from  this  point  to  each  end  of  the  axis 
as  a  check  on  the  computed  values. 

Field  Notes:  1.  Make  a  large,  open  sketch  showing  the  base 
lines,  the  axis  of  the  bridge,  the  values  of  all  angles  measured 
and  the  values  of  all  angles  turned  off  in  the  location  of  the 
pier.  2.  Keep  the  field  notes  for  the  triangulation  according 
to  the  form  on  p.  197.  3.  Arrange  computations  for  trian- 
gulation according  to  the  form  on  p.  399,  or,  better  still,  that  on 
p.  400.  The  form  used  in  determining  the  probable  error  of 
the  base  line  is  given  on  p.  59. 

Suggestions:  1.  Select  a  place  for  this  exercise  where  the  stakes  for 
each  base  line  may  be  set  with  their  tops  on  a  level.  As  considerable 
time  is  necessary  for  setting  these  stakes,  they  may  be  driven  once  for  all 
and  used  by  different  parties.  The  work  may  be  further  shortened  by 
permitting  one  party  to  work  on  one  side  of  the  imaginary  river  and  the 
other  party  to  work  on  the  other  side.  The  work  may  be  changed  for 
different  parties  by  changing  slightly  the  lengths  of  the  base  line  or  the 
distance  between  the  two  stakes  A  and  B.  When  the  time  comes  for 
establishing  the  center  of  the  pier,  it  will  be  convenient  to  do  this  on  a 
board  platform  (a  table  turned  upside  down  will  answer  the  purpose). 

2.  If  desired,  the  triangulation  for  determining  the  length  of  the  axis 
AB  may  be  done  on  one  day,  the  necessary  computations  made  in  the 
evening,  and  the  angles  turned  off  for  locating  the  pier  on  another  day. 
Of  course,  if  time  permits,  two  or  more  piers  may  be  located  instead  of  one. 

Questions:  1.  Give  the  two  steps  involved  in  locating  a 
bridge  pier,  p,  216,  §  275.  2.  Give  an  ideal  method.  §  275  (a). 


SPECIAL   PROBLEMS   IN   TRANSIT   SURVEYING.      49 

3.  Is  this  method  often  practicable?  4.  Give  the  general 
method.  §  275  (b).  5.  Why  is  it  undesirable  to  choose  both 
base  lines  on  the  same  shore  and  on  the  same  side  of  the  bridge, 
or  on  opposite  shores,  one  above,  the  other  below  the  bridge? 
6.  Why  is  it  not  worth  while  to  lay  off  the  base  line  at  right 
angles  to  the  axis?  7.  Give  suggestions  for  referencing  and 
protecting  hubs.  p.  217.  8.  Give  suggestions  for  choosing  the 
location  and  the  length  of  a  base  line.  pp.  217  and  193.  9.  When 
there  are  several  piers,  are  they  always  located  from  the  same 
point  on  a  base  line?  p.  217.  10.  What  is  done  when  the  con- 
ditions on  the  shore  are  unfavorable  for  base-line  measurement? 
p.  217.  11.  What  should  be  the  limit  of  error  for  the  sum  of 
the  most  probable  values  of  the  three  angles  in  each  of  the  main 
triangles?  p.  218.  12.  Describe  the  method  for  laying  off  the 
angles,  p.  218.  13.  When  a  pier  is  built  in  a  movable  caisson, 
how  is  the  latter  kept  in  place?  14.  How  does  the  method  of 
giving  points  for  a  rectangular  pier  differ  from  that  used  for 
round  piers?  p.  218. 

Exercise  Tp-10. 
To  Stake  Out  a  Circle  with  a  Transit  and  a  Tape. 

Reference:     Page  204,  §  263. 

Equipment:  Transit,  steel  tape,  ax,  and  stakes 

Directions:  Stake  out  a  complete  circle  whose  radius  (prefer- 
ably not  less  than  300  feet)  will  be  given  by  the  instructor. 

Field  Notes:  1.  All  computations  neatly  arranged  on  the 
right-hand  page.  2.  Before  beginning  to  stake  out  the  curve, 
work  up  the  field  notes  in  a  form  similar  to  that  for  deflection 
angles  on  p.  174.  See  also  suggestion  (3),  p.  207. 

Suggestions:  In  this  exercise  C  may  be  taken  as  100  feet,  and  R  is  given, 
hence  D  is  easily  calculated.  In  the  field  work,  follow  the  general  method 
outlined  in  step  (4),  p.  206,  and  also  the  directions  for  "picking  up"  a 
tangent,  p.  206. 

If  desired,  additional  exercises  may  be  given,  as,  for  example,  to  connect 
two  tangents  by  a  circular  arc  (see  p.  206,  §  263  (/)).  If,  however,  the 
student  is  to  have  a  course  in  railroad  curves,  it  is  better  to  do  all  such 
work  in  connection  with  that  course. 

Questions:  1.  Define  tangent,  angle  of  intersection,  deflection 
angle,  and  chord.  2.  Prove  that  T  =  R  X  tan  £  7.  3.  Prove 
that  sin  D  =  $  C  +  R.  4.  Prove  that  T  =  (C  X  tan  $  7) 


50     SPECIAL  PROBLEMS  IN   TRANSIT   SURVEYING. 

-T-  2  sin  D.  5.  Define  sub-chord,  sub-deflection  angle,  length 
pf  curve,  and  degree  of  curve.  6.  How  is  the  length  of  curve 
usually  found?  7.  What  is  the  degree  of  curve  in  this  exer- 
cise? 8.  What  is  the  length  of  curve  in  this  exercise?  9.  If 
50-foot  chords  were  used  in  this  exercise,  what  would  be  the 
new  values  for  the  deflection  angle  and  the  sub-deflection  angle? 
10.  Describe  the  general  method  of  running  in  a  circular  curve 
between  two  tangents,  p.  206.  11.  Explain  the  method  of 
"picking  up"  a  tangent,  giving  two  rules  to  be  kept  in  mind, 
p.  206.  12.  Prove  that  if  a  transit  is  at  3,  the  backsight  at  2, 
and  the  vernier  at  2  D,  the  line  of  sight  may  be  made  tangent 
to  the  curve  by  setting  the  vernier  at  3  D.  13.  Why  should 
the  index  reading  for  P.T.  equal  %  11 


GROUP   L. 

EXERCISES   IN  LEVELING. 

The  first  five  exercises  in  this  group  offer  the  student  an  opportunity  to 
learn  the  use  of  the  level  and  the  leveling  rod,  and  to  study  the  sources  of 
personal  and  instrumental  errors.  The  next  three  exercises  afford  practice 
in  differential  leveling  and  in  profile  leveling,  while  the  ninth  exercise  is  a 
class-room  discussion  of  errors  in  leveling.  The  remaining  three  exercises 
take  up  the  use  of  the  hand  level,  trigonometric  leveling  and  barometric 
leveling. 

Exercise  L  1. 
Setting  up  the  Level. 

References:  Page  226,  also  544. 

Equipment:  A  level  for  each  student,  or  as  many  levels  as  are 
available. 

Directions:  1.  Set  up  a  level  as  directed  on  p.  226.  2.  Per- 
form each  of  the  three  steps  in  the  experiment  described  on 
p.  227. 

Questions:  1.  What  is  the  shape  of  the  interior  surface  of  the 
glass  tube  of  a  spirit-level?  p.  544.  2.  Upon  what  does  the 
sensitiveness  of  a  bubble  depend?  p.  544.  3.  Can  a  bubble  be 
too  sensitive  for  ordinary  work?  4.  What  is  the  fluid  used  for 
the  level-bubble?  p.  544.  5.  Why  does  the  length  of  the 
bubble  change  from  time  to  time,  and  is  it  more  sensitive  when 
long  or  when  short?  p.  544.  6.  What  is  the  axis  of  a  bubble  tube? 
p.  544.  7.  What  should  be  the  first  precaution  taken  in  setting 
up  a  level?  p.  251,  §  322,  also  271,  §  349.  8.  If  it  is  impossible  to 
set  up  a  level  so  that  the  bubble  will  remain  in  the  center  for 
all  positions  of  the  telescope,  what  does  this  indicate? 

Additional  Questions:  Many  of  the  questions  asked  in  Exer- 
cise T-l  (Setting  up  the  Transit)  may  also  be  asked  in  connection 
with  setting  up  the  level.  If  the  construction  of  the  telescope 
has  not  already  been  discussed  in  connection  with  transit  work, 
the  instructor  should  explain  briefly  the  different  parts  of  the 
telescope  (see  photograph,  p.  551),  or,  if  thought  best,  to  add  to 
the  questions  given  above  those  on  pages  96  and  97  of  this  book. 

51 


52  EXERCISES  IN   LEVELING. 

Exercise  L  2. 
Reading  the  Leveling  Rod. 

References:   Pages  227  to  232. 

Equipment:  Several  leveling  rods  for  each  squad,  including 
targets  with  scales  and  targets  with  verniers. 

Directions:  1.  Set  the  target  at  random  without  extending 
the  rod.  Read  and  record  the  setting  of  the  target.  2.  Record 
the  instructor's  reading.  3.  Repeat  for  a  number  of  settings 
for  a  "low  rod."  4.  Apply  to  each  rod  the  two  tests  described 
in  §  286,  p.  232.  5.  Read  and  record  several  settings  for  a 
"high  rod." 

Suggestions:  It  is  well  for  an  instructor  to  set  the  targets  at  random  on 
several  rods,  and  to  require  the  members  of  his  squad  to  read  these  settings 
in  rotation.  He  should  take  pains  to  have  some  of  the  settings  near  the 
"danger  points"  where  are  likely  to  occur  such  common  mistakes  as  are 
noted  at  the  bottom  of  p.  229  and  on  p.  231.  The  exercise  should  be 
continued  until  each  member  of  the  squad  can  read  any  target  setting,  for 
either  a  "low"  or  a  "high  "  rod. 

Questions:  1.  What  two  methods  are  there  of  reading  a  rod 
in  leveling?  §  281,  p.  227.  2.  What  is  the  difference  between  a 
target  with  a  scale  and  a  target  with  a  vernier?  3.  How  can 
you  estimate  a  reading  to  thousandths  on  a  target  with  a 
scale?  4.  What  are  some  of  the  common  mistakes  in  reading  a 
leveling  rod,  and  what  points  should  be  fixed  in  mind  as 
"danger  points"?  p.  229.  5.  Explain  the  difference  between 
the  methods  of  reading  a  target  with  a  scale  and  a  target  with  a 
vernier.  §  285.  6.  Explain  how  to  read  a  "high  rod,"  and  the 
tests  which  should  be  applied  to  every  rod  when  using  it  for 
the  first  time.  §§  284  and  286.  7.  What  are  the  different 
sources  of  error  or  mistakes  in  taking  a  "high  rod"  reading? 
§  284  (a),  (b).  8.  Into  what  two  classes  may  leveling  rods  be 
divided?  p  571.  9.  Explain  the  difference  between  the  New 
York  and  the  Philadelphia  rods.  10.  What  kind  of  target  is 
preferable  for  long  sights?  p.  572.  11.  What  is  an  angle 
target,  and  for  what  purpose  was  it  designed?  p.  572  and  p.  270. 

12.  Name  two  special  forms  of  leveling  rods.  p.  572,  §  573  (b). 

13.  Describe  a  plumbing  level,  p.    573.     14.    Could  stadia  rods, 
p.  574,  be  used  as  self-reading  leveling  rods? 


EXERCISES    IN   LEVELING.  53 


Exercise  L-3. 

To  Find  the  Probable  Error  of  Sighting  and  of  Setting 
a  Target. 

Reference:   Page  270,  §  348. 

Equipment:  Level,  leveling  rod,  tape,  ax,  stakes. 

Directions:  1.  Set  up  the  level,  and  drive  stakes  approxi- 
mately in  line,  at  distances  of  100,  200,  300,  and  400  feet 
respectively  from  the  level.  2.  Hold  the  rod  on  the  stake  at 
the  100-foot  point,  set  the  target  so  that  its  center  coincides 
with  the  line  of  sight,  and  record  the  reading.  3.  Move  the 
target  up  or  down  a  foot  or  more  out  of  the  line  of  sight  and 
again  set  it  as  accurately  as  possible,  holding  the  rod  on  the  same 
point  on  the  stake.  4.  Repeat  the  work  until  five  independent 
settings  of  the  target  have  been  made  on  each  of  the  four  stakes. 
5.  From  the  five  readings  at  each  stake  find  the  probable  error 
for  that  stake  as  explained  on  pp.  15  to  19. 

Field  Notes:  Record  the  readings  for  the  different  stakes  in 
separate  columns.  Use  the  form  on  p.  19  for  determining  the 
probable  errors.  Arrange  all  computations  systematically. 

Suggestions:  Set  two  legs  of  a  tripod  in  a  line  parallel  to  the  general 
direction  of  the  line  of  stakes,  and  see  that  all  three  legs  are  reasonably  firm 
before  leveling  up.  When  the  sun  is  shining  set  the  level  up  in  the  shade. 
Take  every  precaution  to  avoid  disturbing  the  level  during  the  exercise, 
and  be  careful  to  have  the  bubble  in  the  center  of  the  tube  during  each 
sight.  The  bubble  may  often  be  brought  into  the  center  by  pressing 
down  slightly  with  the  finger  on  the  telescope. 

Questions:  1.  Give  some  of  the  sources  of  error  in  sighting. 
p.  270.  2.  What  is  the  effect  of  refraction?  p.  273.  3.  What 
is  the  best  time  of  day  for  precise  leveling?  Bottom  of  p.  272, 
also  (3)  p.  278. 

Note:  This  exercise  may  be  repeated,  the  readings  being  made  directly 
from  the  level  without  the  use  of  the  target.  The  probable  errors  at  each 
distance  for  the  two  methods  may  then  be  compared,  thus  giving  an  idea 
of  the  relative  accuracy  of  target  readings  and  of  direct  readings.  See 
p.  271. 


54  EXERCISES   IN   LEVELING, 

Exercise  L-4. 

Comparison  of  Readings  Taken   With    and    Without 
the  Target. 

Reference:  Experiment,  p.  271. 

Equipment:  Level,  leveling  rod,  tape,  ax,  and  stakes. 

Directions:  1.  Set  up  the  level,  and  drive  stakes  at  dis- 
tances of  50,  100,  150,  200,  250,  300,  350,  and  400  feet  from  the 
level.  2.  Take  a  rod  reading  on  the  top  of  each  stake,  first 
without,  then  with,  the  target.  3.  Record  all  readings  and 
state  conclusions  as  to  how  closely  one  can  read  at  different 
distances  without  using  the  target,  and  how  such  readings  are 
affected  by  distance. 

Note:  Conclusions  should  not  be  drawn  from  too  few  data,  but  by  tabu- 
lating the  results  obtained  by  all  the  members  of  a  class  a  comparison  of 
the  two  methods  of  reading  the  rod  may  be  made. 

Exercise  L-5. 

To  Test  the  Sensitiveness  of  a  Level  Bubble. 

Reference:  Page  545,  §  567  (a). 

Equipment:  Level,  leveling  rod,  tape,  ax  and  stakes. 

Directions:  1.  Set  up  the  level,  and  drive  a  stake  200  feet 
away.  Test  the  sensitiveness  of  the  bubble  with  the  leveling 
rod  held  on  this  stake  as  explained  on  p.  545.  2.  Repeat  the 
test,  holding  the  rod  at  distances  of  300  and  400  feet  from  the 
level. 

Field  Notes:  A  complete  record  of  the  results  obtained  from 
the  different  tests  with  the  mean  value  of  one  division  in 
seconds  of  arc. 

Suggestions:  See  page  545. 

Questions:  1.  How  could  a  bubble  tube  other  than  a  telescope 
level  be  tested?  p.  545.  2.  What  is  a  level-trier?  3.  Show  by 

means  of  a  sketch  that  R  —  -r-  D,  p.  545.     4.   Find  the  radius 

of   curvature   of  the   bubble  tube  on    the  level  used  in  this 
exercise. 


BXEECISES   IN   LEVELING.  55 

Exercise  Lr6. 
Differential  Leveling. 

(A  Study  of  the  Theory.) 

References:  Pages  234  to  242. 

Equipment:  Level,  leveling  rod. 

Directions:  1.  Select  two  points  several  hundred  feet  apart, 
one  of  them  40  or  50  feet  higher  than  the  other.  2.  Run  a 
line  of  levels  from  the  first  point  to  the  second  and  back  again 
to  the  first  point. 

Field  Notes:  Use  Form  B  on  p.  240. 

Suggestions:  For  this  first  exercise  in  differential  leveling,  it  is  well  to 
choose  a  place  where  a  complete  circuit  can  be  made  in  five  or  six  set- 
ups. The  work  may  then  be  repeated,  the  levelman  and  the  rodman 
interchanging  positions.  Too  much  emphasis  should  not  be  placed  on 
the  niceties  of  field  work,  as  the  object  of  this  exercise  is  to  acquaint  the 
student  with  the  theory  of  leveling.  In  the  next  exercise  the  methods  of 
field  work  may  be  studied,  and  greater  precautions  taken  to  obtain  accurate 
results. 

Before  going  into  the  field,  it  is  well  for  the  instructor  to  put  a  sketch  on 
the  blackboard  similar  to  that  on  page  238,  with  backsight  and  foresight 
readings  indicated  in  simple  numbers,  and  then  to  require  each  student  to 
work  out  the  notes  for  this  sketch  in  a  form  similar  to  that  on  page  240. 
It  is  also  well  to  discuss  the  questions  given  below  just  before  beginning  the 
field  work  of  this  exercise. 

Questions:  1.  What  two  kinds  of  work  are  done  in  leveling? 
p.  234,  §  288.  2.  Define  datum  line  and  datum  plane.  3.  Is 
a  level  surface  a  plane  surface?  4.  What  is  taken  as  a  con- 
venient datum  the  world  over?  5.  Is  the  sea  level  the  only 
datum  used?  6.  Define  bench  or  bench-mark.  7.  Define 
station,  and  point  out  the  difference  between  a  station  in  transit 
surveying  and  a  station  in  leveling.  8.  Define  plane  of  sight. 

9.  What    are    the    two    essential    steps    in    leveling?    p.  235. 

10.  Is  there  any  difference  in  practice  between  measuring  up  to 
the  plane  of  the  sight  and  measuring  down?    11.    Define  height 
of  instrument.     12.    Define  backsight.     13.    How  is  a  backsight 
used  in  determining  height  of  instrument?    14.    Define  foresight. 
15.    Why  are  "backsight"  and  "foresight  "  unfortunate  terms? 
p.  237.     16.   What  two  terms  are  sometimes  used  in  place  of 
backsight  and  foresight?  17.    What  is  the  object  of  backsight- 
ing  and  of  foresighting?  p.   237.     18.   What  abbreviations  are 


56  EXERCISES   IN   LEVELING. 

used  in  leveling?  19.  What  two  formulas  express  the  theory  of 
leveling,  and  to  what  two  steps  in  leveling  do  they  correspond? 
p.  237.  20.  Explain  how  the  elevations  of  points  above  the 
plane  of  sight  may  be  found.  21.  Explain  by  means  of  a 
sketch  the  general  theory  of  leveling  when  more  than  one  set- 
up is  necessary.  §  299  (c).  22.  Are  stations  in  leveling 
necessarily  in  a  straight  line,  or  may  they  be  taken  anywhere? 
23.  How  may  the  two  steps  in  leveling  be  remembered? 
Remark,  p.  238.  24.  What  is  an  intermediate  station  and  its 
distinguishing  characteristic?  p.  238.  25.  What  is  a  turning- 
point,  its  distinguishing  characteristic,  and  how  did  it  get  its 
name?  26.  May  a  station  or  a  bench-mark  be  used  as  a  turning- 
point?  p.  239.  27.  What  are  the  first  and  last  points  sighted 
at  in  leveling  usually  considered?  p.  239.  28.  Explain  why  an 
error  made  at  a  turning-point  is  much  more  serious  than  an 
error  made  at  an  intermediate  station.  29.  What  are  the 
advantages  and  disadvantages  of  Form  A  for  leveling  notes? 
p.  239.  30.  Comment  on  Form  B  for  leveling  notes,  p.  240. 


Exercise  L-7. 
Differential  Leveling. 

(A  Study  of  Field  Methods.) 

References:  Pages  248-258;  260-263. 
Equipment:  Level,  leveling  rod,  ax. 

Directions:  From  some  assumed  point  as  a  bench-mark  run 
a  line  of  levels  to  a  second  point  and  return,  making  a  circuit 
of  about  10  set-ups.  Keep  field  notes  according  to  Form  B, 
p.  240. 

Suggestions:  The  theory  of  leveling  having  been  studied  in  the  pre- 
ceding exercise,  special  attention  should  be  paid  in  this  exercise  to  the 
methods  of  field  work,  especially  to  those  precautions  which  are  necessary 
for  accurate  work.  If  desired,  several  parties  of  two  men  each  may  run 
levels  over  the  same  circuit,  checking  every  three  or  four  set-ups  at  a  com- 
mon bench-mark  established  by  the  instructor.  It  is  well  to  establish  a 
number  of  permanent  bench-marks  differing  as  much  as  practicable  in  ele- 
vation, as  these  benches  will  be  of  use  later  in  the  course  in  connection 
with  barometric  leveling,  trigonometric  leveling,  and  other  exercises.  If 
'desired,  this  exercise  may  be  repeated,  all  sights  being  taken  on  a  self- 
reading  rod,  no  use  being  made  of  the  target. 


EXERCISES  IN  LEVELING.  57 

Questions:  1.  Give  the  signals  used  in  leveling,  p.  248. 
2.  How  may  the  elevation  of  the  starting-point  be  obtained? 
p.  249.  3.  How  may  any  elevation  be  assumed  and  the  notes 
afterward  corrected?  Illustration,  p.  250.  4.  Why  should  the 
rodman  hold  his  rod  a  second  time  after  clamping  the  target? 
5.  What  should  be  the  lengths  of  foresights  and  backsights  in 
ordinary  work  for  the  best  results?  6.  What  is  the  first  pre- 
caution in  setting  up  a  level?  p.  251.  7.  In  going  up,  or  down, 
hill,  how  can  one  avoid  taking  unequal  sights?  8.  What  is  a 
common  mistake  of  the  beginner  in  setting  up  a  level  on  steep 
slopes,  and  how  can  this  mistake  be  avoided?  p.  251.  9.  What 
chiefly  determines  the  location  of  turning-points?  p.  252. 
10.  In  choosing  an  object  for  a  turning-point,  what  should  be 
kept  in  mind?  Remark,  p.  252.  11.  Describe  a  form  of  turning- 
point  sometimes  used.  §  323  (b).  12.  Describe  two  methods 
of  holding  a  leveling  rod.  p.  252.  13.  Give  a  method  of 
making  sure  that  the  rod  is  plumb,  pp.  252,  270,  §  346  (c). 
14.  Give  examples  of  bench-marks  both  permanent  and  tem- 
porary, p.  253.  15.  Where  should  bench-marks  be  established? 
p.  253.  16.  What  is  the  only  method  of  checking  field  work 
in  leveling?  §  329.  17.  If  sixteen  set-ups  are  necessary  to 
complete  a  circuit  of  levels,  what  should  be  the  approximate 
limit  of  error?  i.e.,  the  difference  between  the  elevation  of  the 
starting-point  and  the  elevation  of  the  same  point  as  deter- 
mined at  the  completion  of  the  circuit,  p.  254.  18.  Give 
some  suggestions  for  working  rapidly  in  leveling,  p.  255. 
19.  What  should  be  the  average  speed  for  class  work?  Remark, 
p.  255.  20.  Give  suggestions  for  the  levelman  concerning  the 
following  points:  p.  260.  Choosing  place  for  level;  leveling  on 
steep  slopes;  watching  the  bubble;  unnecessary  clamping; 
horizontal  cross-hair;  sunshade;  disturbing  instrument ;  definite 
signals;  adjustment  of  level;  effects  of  heat  and  wind;  care  of 
the  level.  21.  Give  suggestions  for  the  rodman  concerning  the 
following  points:  See  p.  261.  Choosing  turning-points;  length 
of  sights;  holding  the  rod;  moving  the  target;  clamping  the 
target;  testing  the  rod;  common  mistakes  in  reading;  care  of 
the  rod.  22.  Give  duties  of  levelman;  of  rodman.  p.  263. 


58  EXERCISES    IN    LEVELING. 

Exercise  L-8. 
Profile  Leveling. 

References:  Page  242,  §  306;   p.  251. 

Equipment:  Level,  leveling  rod,  stakes,  tape. 

Directions:  Drive  a  row  of  stakes  50  feet  apart  for  a  distance 
of  about  1000  feet.  Run  a  line  of  profile  levels,  taking  the 
elevation  of  the  ground  at  each  stake.  At  all  intermediate 
stations  read  the  rod  from  the  instrument  without  the  use  of 
the  target,  but  at  turning-points  use  the  target.  When  the 
elevation  at  the  last  stake  has  been  determined,  run  back  over 
the  line  to  the  starting-point,  taking  turning-points  only,  and 
thus  checking  the  work  of  the  whole  exercise. 

Field  Notes:  Keep  field  notes  according  to  Form  E,  p.  256, 
and  check  the  arithmetical  work  by  the  method  explained  on 
p.  242. 

Suggestions:  If  desired,  several  parties  of  two  men  each  may  work  along 
the  same  line  of  stakes,  checking  at  frequent  intervals  on  the  same  bench- 
marks established  by  the  instructor.  In  this  case  it  will  be  unnecessary  to 
run  back  over  the  line  as  a  check. 

Questions:  1.  What  is  an  intermediate  station?  p.  238. 
2.  Is  it  necessary  to  take  the  elevations  at  intermediate 
stations  as  accurately  as  at  turning-points?  3.  Does  the  rule 
for  checking  notes  on  p.  242  afford  any  check  for  intermediate 
stations?  4.  Explain  a  form  of  notes  that  does  give  a  check  on 
intermediate  stations.  §  303  (e).  5.  What  are  the  advantages 
of  Form  C,  p.  241,  for  profile  notes?  6.  In  ordinary  work  how 
closely  should  the  rod  be  read  at  intermediate  stations,  and 
should  this  reading  be  taken  with  or  without  the  target?  p.  253. 

Exercise  L-9. 
Discussion  of  Errors  in  Leveling. 

(Exercise  for  the  Class-room.) 

Questions:  1.  Give  some  of  the  sources  of  error  in  leveling, 
p.  268.  2.  How  may  the  errors  of  adjustment  be  largely 
eliminated?  3.  What  precautions  should  be  taken  when  the 
bubble  is  sluggish?  p.  268.  4.  What  is  the  error  in  the  move- 


EXERCISES    IN    LEVELING.  59 

ment  of  the  object-glass  slide,  and  how  may  it  be  eliminated? 
p.  268,  also  p.  602,  §  586.  5.  What  is  the  error  due  to  a  defec- 
tive joint  in  the  leveling  rod?  p.  269;  also  Remark,  p.  232. 
6.  Give  some  of  the  sources  of  error  in  manipulating  the  level, 
p.  269.  7.  How  may  the  error  due  to  the  rod  being  held  out  of 
plumb  be  avoided?  8.  Why  is  this  error  compensating  on 
turning-points  when  leveling  up  and  down  hill  over  rolling 
country?  9.  Why  is  this  error  not  compensating  in  leveling 
up  hill  only  or  down  hill  only?  10.  Why  is  it  not  best  to  wave 
the  rod  when  the  reading  is  two  feet  or  less  from  the  bottom  of 
the  rod?  11.  What  errors  are  due  to  the  accumulation  of 
dirt  or  grit  on  the  base  of  the  rod  or  in  the  joints?  12.  Give 
some  of  the  sources  of  error  in  sighting.  13.  Explain  why  the 
settling  of  the  instrument  between  the  backsight  on  one  turning- 
point  and  the  foresight  on  the  next  is  a  source  of  cumulative 
error.  How  may  this  error  be  avoided?  p.  271.  14.  What 
precautions  should  be  taken  to  avoid  errors  due  to  disturbance 
of  the  instrument?  p.  272.  15.  Explain  why  the  settling  of 
the  turning-point  is  a  source  of  cumulative  error.  16.  Explain 
why  the  sun  shining  on  the  instrument  is  a  source  of  cumula- 
tive error,  p.  273.  17.  What  is  the  error  due  to  curvature? 
p.  272.  18.  What  is  the  error  due  to  refraction?  p.  273. 

19.  What  is  the  effect  of  combining  these  two  errors?  p.  273. 

20.  Give    common    mistakes     in     recording.     21.    How     may 
errors    in    computing    be     discovered?  p.  274.     22.    How  may 
personal  errors  be  partially  eliminated?     23.    Recapitulate  the 
most  important  precautions  taken  to  eliminate  errors:    (a)  mis- 
takes;      (b)  constant     errors;       (c)  accidental     errors,  p.  275. 

24.  How    may    the    precision    of    leveling    be    judged?  p.  275. 

25.  How  may  the  total  error  of  a  line  of  levels  be  expected  to 
vary?  p.  276.     26.    In  a  common  formula  for  allowable  error 
what  is  the  usual  value  of  C?  p.  276.     27.    If  a  circuit  of  levels 
four  miles  long  be  completed,  what  should  be  the  permissible 
error  if  the  coefficient  C  is   .04?    28.    Give  some  of  the  most 
important    directions    contained    in    instructions    for    accurate 
leveling  (p.  277)  as    regards:    number   of    rodmen;    method  of 
rodmen    keeping    independent    readings;     weather    conditions; 
foresights  and  backsights;   duties  of  the  bubble  tender;   adjust- 
ment of   level;    steel  turning-points;    plumbing  levels;    perma- 
nent bench-marks;    permissible  error.     29.    Give  the  method  of 
procedure    when    two    rodmen    are    employed,  p.  279.     30.    In 


60  EXERCISES    IN   LEVELING. 

crossing  a  wide  river  explain  how  the  method  of  reciprocal 
leveling  may  be  used.  p.  243.  (See  also  exercise  in  reciprocal 
leveling,  page  63  of  this  book.) 

Exercise  L-10. 

Use  of  the  Hand  Level. 

Reference:  Page  233. 

Equipment:  Hand  level  and  hand  leveling  rod,  or  two  hand 
levels  and  two  rods. 

Directions:  Find  the  difference  in  elevation  between  two 
points  several  hundred  feet  apart,  by  means  of  a  hand  level, 
using  the  second  method  of  §  287,  p.  233. 

Field  Notes:  A  sketch  showing  the  different  steps  and  the 
final  difference  in  elevation. 

Suggestions:  If  possible,  the  leveling  should  be  done  between  two  bench- 
marks whose  elevations  have  been  determined  previously  by  differential 
leveling,  and  the  difference  in  elevation  should  be  compared  with  that 
obtained  by  the  more  accurate  method.  The  party  should  consist  of  two 
men;  and,  if  desired,  each  may  be  equipped  with  a  hand  level  and  a  5  foot 
rod,  so  that  first  one  and  then  the  other  uses  the  hand  level,  alternating, 
as  explained  in  "Routine  of  the  Field  Work.''  bottom  of  p.  351.  If  only 
one  hand-level  is  used,  the  work  may  be  repeated,  the  levelman  and  rod- 
man  interchanging  positions,  and  running  back  over  the  line  to  the  start- 
ing-point. 

Questions:  1.  How  can  rough  work  be  done  without  the  use 
of  a  rod?  p.  233.  2.  What  is  the  difference  in  method  between 
leveling  up  hill  and  leveling  down  hill?  p.  233.  3.  For  what  is 
the  hand  level  chiefly  used?  p.  233. 

Exercise  I/-11. 
Trigonometric  Leveling. 

References:  Pages  244,  264. 

Equipment:  Transit,  leveling  rod,  and  steel  tape. 

Directions:  1.  Find  the  difference  in  elevation  between  two 
points  A  and  B,  by  setting  up  the  transit  near  A  and  using  the 
first  method  of  "Trigonometric  Leveling"  on  pp.  244,  264. 
2.  Repeat  the  exercise,  setting  up  the  transit  near  B  instead  of 
A,  the  two  men  in  the  party  interchanging  positions. 


EXERCISES   IN   LEVELING.  61 

Field  Notes:  A  sketch  showing  the  method,  with  all  distances 
and  angles;  also  all  computations  systematically  arranged. 

Suggestions:  1.  In  this  exercise  the  horizontal  distances  from  the  tran- 
sit to  each  of  the  two  points  A  and  B  is  measured  with  a  tape,  although  in 
most  field  work  where  this  method  is  used,  distances  are  found  either  by 
triangulation  or  with  the  stadia.  If  possible,  the  two  points  A  and  B 
should  be  bench-marks  whose  elevations  have  been  determined  previously 
by  spirit  leveling,  and  the  difference  in  elevation  obtained  in  this  exercise 
should  be  compared  with  that  obtained  by  spirit  leveling.  2.  The  shortest 
method  is  to  set  the  transit  up  with  the  end  of  the  supporting  axis  approxi- 
mately over  either  A  or  B.  If  this  is  impracticable,  it  will  be  necessary 
to  determine  the  height  of  the  supporting  axis  by  a  backsight  on  the  nearer 
station.  See  Remark  (b),  p.  244. 

Questions:  1.  Explain  the  first  method  of  trigonometric 
leveling,  p.  244.  2.  In  this  method,  if  elevations  of  points  are 
required  with  reference  to  some  datum,  what  is  the  first  step 
after  setting  up  the  transit?  p.  244.  3.  If  the  horizontal  dis- 
tances from  the  transit  to  the  point  whose  elevation  is  required 
cannot  be  measured  directly,  how  would  you  proceed?  p.  244. 
(See  also  Exercise  for  Determining  the  Height  of  an  Inac- 
cessible Point,  p.  223.)  4.  In  finding  the  elevation  of  any 
point  on  the  ground  with  reference  to  a  point  under  the  transit, 
how  would  you  use  a  sight-pole  in  place  of  a  leveling  rod? 
p.  264,  Practical  Hint  (a).  5.  How  may  time  be  saved  in 
computing  elevations  from  vertical  angles?  p.  264.  6.  Show 
what  error  may  be  expected  for  sights  of  200  feet  if  the  hori- 
zontal distance  is  correct  but  the  error  in  the  vertical  angle  is 
one  minute,  ignoring  instrumental  errors,  p.  264.  7.  For  the 
same  length  of  sight,  what  would  be  the  error  if  the  vertical 
angle  of,  say,  8  degrees  40  minutes  is  correct,  but  the  horizontal 
distance  is  in  error  as  much  as  one  foot?  p.  264.  8.  Explain 
the  second  method  of  trigonometric  leveling,  p.  264.  9.  Is  the 
first  or  the  second  method  most  used  in  topographic  surveying, 
and  how  are  the  distances  determined?  p.  264.  10.  How  may 
triangulation  and  trigonometric  leveling  be  combined,  and  how 
do  the  results  compare  with  spirit  leveling?  p.  200. 


62  EXERCISES   IN   LEVELING. 

Exercise  L-12. 
Barometric  Leveling. 

References:  Page  245,  §  313;  p.  265,  §  343. 

Equipment:   Aneroid  barometer,  thermometer. 

Directions:  1.  Hold  the  barometer  on  a  bench-mark  whose 
elevation  has  been  determined  previously  by  spirit  leveling, 
and  set  the  altitude  scale  of  the  barometer  to  correspond  to 
the  elevation  of  that  bench-mark.  2.  Without  disturbing  the 
altitude  scale  take  readings  of  the  barometer  at  two  or  more 
bench-marks  whose  elevations  are  known,  and  compare  the 
elevations  as  found  by  the  barometer  with  the  elevations  as 
found  by  spirit  leveling.  3.  Repeat  the  problem  but  ignore  the 
altitude  scale,  and  proceed  as  directed  on  p.  265,  §  343  (a). 
4.  Compare  results  with  those  obtained  by  spirit  leveling  and 
with  those  found  by  the  use  of  the  altitude  scale. 

Field  Notes:  Keep  a  full  record  in  tabular  form  of  the  read- 
ings of  the  altitude  scale,  of  the  barometer  readings  in  inches, 
and  of  the  temperature  at  each  bench-mark.  Also  a  systematic 
arrangement  of  the  computations  for  reducing  readings  to 
altitudes. 

Suggestions:  In  this  exercise  it  is  desirable  that  there  should  be  a  con- 
siderable difference  in  elevation  between  the  successive  bench-marks 
selected,  and-  that  these  elevations  should  have  been  determined  pre- 
viously by  spirit  leveling.  The  results  as  obtained  by  different  students 
going  over  the  same  line  of  bench-marks  may  be  tabulated  by  the 
instructor  and  shown  to  the  class,  thus  giving  an  idea  of  the  accuracy  to 
be  obtained  in  barometric  leveling.  It  is  well  also  to  use  several  different 
aneroid  barometers,  and,  if  desired,  readings  may  also  be  taken  with  mer- 
curial barometer. 

Questions:  1.  Describe  the  aneroid  barometer,  p.  264.  2. 
What  is  the  average  reading  of  a  barometer  at  sea  level, 
and  the  average  rate  of  fall  in  ascending  above  the  sea  level? 
p.  245.  3.  What  are  the  atmospheric  sources  of  error?  p.  245. 

4.  How   does   temperature   affect   barometer   readings?  p.  246. 

5.  Compare  two  classes  of  barometric  formulas,  p.  246.     6.   In 
ordinary    work    what    sources    of    error    are    usually    ignored? 
Bottom    p.    246.      7.    What    are    some    of    the    instrumental 
sources   of   error?  p.  265.     8.    Give   the   method    of   procedure 
where  single   observations   are  taken,  p.  265.     9.    Explain  the 
method   of   simultaneous    observations,  p.  266.     10.    What   are 
the  ordinary  limits  of  error?  p.  267. 


GROUP  LP. 

SPECIAL  PROBLEMS  IN  LEVELING. 

The  exercises  in  this  group  deal  with  various  problems  in  leveling  such  as 
setting  grade  stakes,  estimating  cut  and  fill  for  grading,  and  staking  out  a 
vertical  curve. 

Exercise   Lp-1. 

Reciprocal  Leveling. 

Reference:   Page  243. 

Equipment:   Level,  leveling  rod,  ax,  and  stakes. 

Directions:  1.  Drive  two  stakes  A  and  B  from  300  to  400 
feet  apart.  2.  Imagine  these  stakes  to  be  on  opposite  banks  of 
a  river  so  that  the  level  cannot  be  set  up  between  them,  and 
find  the  difference  in  elevation  between  the  tops  of  the  stakes 
by  the  method  of  Reciprocal  Leveling,  p.  243.  3.  Repeat  the 
work,  levelman  and  rodman  interchanging  positions.  4.  Set  up 
the  level  approximately  one-half  way  between  the  two  stakes, 
and  check  the  mean  result  obtained  by  reciprocal  leveling. 

Field  Notes:  Make  a  sketch  showing  the  approximate  dis- 
tance between  stakes  as  obtained  by  pacing,  the  positions  of 
the  level  and  all  elevations.  See  Figure,  p.  598.  In  addition 
keep  the  level  notes  on  the  left-hand  page  in  the  usual  form, 
p.  240. 

Questions:  1.  Why  does  reciprocal  leveling  tend  to  eliminate 
the  error  due  to  adjustment,  the  error  due  to  curvature,  and 
refraction?  pp.  598,  599,  273. 

Exercise  Lp-2. 
To  Set  Stakes  on  a  Grade  Between  Two  Fixed  Points. 

(Special  Method.) 

References:  Page  243,  §  310;  p.  258,  §  334;  p.  280,  §  357; 
p.  282,  §  358. 

Equipment:   Level,  leveling  rod,  ax,  and  stakes. 
Directions:    Choose  a  place  where  the  slope  of  the  ground  is 
63 


64  SPECIAL   PROBLEMS  IN   LEVELING. 

uniform  for  several  hundred  feet  so  that  the  tops  of  all  stakes 
can  be  driven  to  grade,  and  drive  two  stakes  A  and  B  several 
hundred  feet  apart.  2.  Ascertain  the  difference  in  elevation 
between  A  and  B.  3.  Set  a  line  of  stakes  with  their  tops  on 
grade  between  A  and  B,  and  with  25-foot  intervals  between 
stakes.  Use  the  grade  rod  method  (see  illustration,  top  of 
p.  281)  and  also  §  358  (a).  4.  Check  the  work  by  setting  up 
the  level  near  stake  A  and  shooting  in  the  grade  as  explained  in 
§  357  (d),  p.  281. 

Field  Notes:  Number  the  stations  0,  0  +  25,  0  +  50,  etc., 
and  keep  the  notes  in  a  form  similar  to  one  of  those  on  pp.  284, 
256. 

Suggestions:    See  Practical  suggestions  on  pp.  259,  282.  and  281. 

Questions:  1.  Define  grade,  and  grade  rod,  and  illustrate  how 
the  grade  rod  is  calculated,  p.  243,  and  also  p.  428.  2.  Give  five 
different  methods  of  setting  grade  stakes,  p.  258.  3.  Give  the 
general  method  of  procedure  in  setting  grade  stakes,  p.  259. 
4.  What  is  the  difference  between  a  true  grade  rod  and  a  field 
grade  rod?  p.  259.  5.  How  close  should  stakes  be  driven  in 
ordinary  grading?  p.  259.  6.  Give  some  practical  suggestions 
for  setting  stakes,  p.  259.  7.  What  are  two  common  mistakes 
which  occur  in  setting  grade  stakes,  and  how  may  errors  be 
detected?  p.  259.  8.  What  additional  columns  should  appear 
in  the  field  notes?  p.  260.  9.  What  is  meant  by  "shooting 
in  "a  grade,  and  what  is  the  best  instrument  to  use  for  this 
method?  p.  260,  also  p.  281.  10.  In  the  method  of  shooting 
in  grades,  why  is  step  4,  p.  281,  necessary,  and  how  can  this 
step  be  avoided?  Note,  p.  281.  11.  What  is  the  object  in 
establishing  a  permanent  foresight  in  step  5,  p.  281?  12.  How 
may  a  convenient  permanent  foresight  be  established?  Sug- 
gestion 2,  bottom  of  p.  281.  13.  Is  the  error  involved  in  set- 
ting the  target  opposite  to  the  center  of  the  object  glass  likely 
to  be  large?  p.  281.  14.  Suppose  the  surface  of  the  ground  to 
have  a  uniform  slope  which,  however,  is  too  far  above  or  below 
the  required  grade  to  permit  driving  stakes  to  grade,  how  would 
you  proceed  to  shoot  in  the  grade?  Suggestion  4,  top  of  p.  282. 
15.  Give  some  practical  suggestions  for  setting  grade  stakes  for 
a  curb.  p.  282.  16.  Give  the  general  method  of  laying  out 
grades  for  pavements  as  regards,  marking  gutter  lines;  center 
line ;  use  of  templet. 


SPECIAL   PROBLEMS   IN    LEVELING.  65 

Exercise  Lp-3. 

To  Set  Grade  Stakes  Between  Two  Fixed  Points 
When  the  Ground  is  Uneven. 

(General  Method.) 

Reference  and  Equipment  same  as  for  preceding  exercise. 

Directions:  Repeat  the  preceding  exercise,  but  select  a  place 
where  the  ground  is  so  uneven  that  the  tops  of  the  stakes 
cannot  be  set  to  grade.  Use  method  2,  p.  258,  i.e.  top  of  each 
stake  to  be  a  whole  number  of  feet  above  or  below  grade. 
Mark  stakes  as  directed  on  p.  260. 

Question:  1.  What  is  the  chief  difference  between  the 
methods  used  in  this  exercise  and  that  of  the  preceding  exer- 
cise? 

Questions  on  Giving  Grades  for  a  Sewer:  2.  Explain  the 
general  method  of  giving  grades  for  a  sewer,  p.  283.  3.  How 
closely  should  grades  be  given  for  a  sewer?  4.  How  would  you 
proceed  when  it  is  impracticable  to  give  elevations  at  equal 
distances  along  sewer  line?  p.  283.  5.  What  rough  check 
should  always  be  employed?  p.  283.  6.  Why  should  bench- 
marks be  established?  p.  283.  7.  Describe  a  form  of  grade- 
pole  for  sewer  work.  p.  283.  8.  Why  work  in  one  direction 
from  down  hill  up  hill  or  vice  versa?  p.  283.  9.  Give  two 
methods  of  measuring  between  grade-slats,  and  why  are 
measurements  made  parallel  to  the  flow  line?  p.  283. 

10.  Explain  in  detail  the  notes  on  pp.  284  and  285.     See  expla- 
nation 286. 

Questions    on    Giving    Elevations   for    a    Line    of    Shafting: 

11.  Give  the  general  method  of  giving  elevations  for  a  line  of 
shafting,  p.  287.     12.    Why  is  it  convenient  to  hold  the  leveling 
rod  upside-down,  and  illustrate  what  is  meant  by  a  minus  grade 
rod?  p.  287. 


66  SPECIAL   PROBLEMS   IN    LEVELING. 

Exercise  Lp-4. 

Use   of  the   Gradienter. 

Reference:   Page  245. 

Equipment:  Transit  equipped  with  a  gradienter,  leveling  rod, 
ax,  and  stakes.  (Transit  should  be  in  adjustment  for  leveling.) 

Directions:  1.  Select  a  comparatively  level  piece  of  ground, 
and  by  means  of  the  gradienter  set  a  row  of  stakes  at  intervals 
of  25  feet  with  their  tops  driven  to  a  given  grade.  2.  Check 
each  stake  by  the  grade-rod  method  explained  on  p.  259. 

Field  Notes:  On  the  right-hand  page  a  description  of  the 
work  with  a  comparison  of  the  levels  obtained  by  the  two 
methods,  and  the  average  discrepancy.  On  the  left-hand  page 
the  usual  form  of  field  notes,  p.  284. 

Suggestion:  This  exercise  may  be  given  in  connection  with  Exercise  Lp-2 
if  desired. 

Questions:  1.  Explain  the  principle  of  the  gradienter.  p.  245. 
2.  How  may  the  gradienter  be  used  for  measuring  distances? 
p.  245. 

Exercise  Lp-5. 

To  Estimate  Cut  and  Fill  for  Grading. 

References:   Page  287,  §  362;  pp.  429-433. 

Equipment:   Level,  leveling  rod,  tape,  ax,  and  stakes. 

Directions:  1.  Select  a  plot  of  ground  at  least  150  feet  square, 
with  a  rather  uneven  surface.  If  no  plot  with  definite  bounda- 
ries is  convenient,  mark  out  one  with  stakes.  2.  Perform  the 
field  work  necessary  to  obtain  data  for  estimating  cut  and  fill 
for  grading  according  to  the  method  of  §  362,  p.  287.  3.  Assum- 
ing that  the  ground  is  to  be  graded  to  a  level  one  foot  below 
the  lowest  elevation  obtained  at  any  stake  set  in  the  preceding 
step,  calculate  the  total  cut  in  cubic  yards. 

Field  Notes:  On  the  right-hand  page  draw  a  sketch  showing 
all  stakes  with  numbers  and  distances,  and  on  the  left-hand 
page  keep  the  level  notes  in  the  usual  form.  p.  240.  Use  a 
system  of  numbering  points  like  that  of  Figure  402  (c),  p.  341. 

Suggestions:  Follow  the  practical  suggestions  given  on  p.  287.  If  desired 
in  the  third  step  above,  the  finished  surface  may  be  assumed  at  such  an 


SPECIAL  PROBLEMS   IN  LEVELING.  67 

elevation  as  to  require  both  .cut  and  fill.  The  problem  may  be  further 
complicated  by  assuming  this  surface  to  be  on  a  slope  instead  of  on  a  level. 
As  a  rule,  however,  the  more  complicated  work  of  calculation  should  be 
left  for  the  course  in  office  work,  and  thus  time  will  be  saved  in  the  field. 

Questions:  Give  the  general  method  of  field  work  in  getting 
data  for  estimating  cut  and  fill  for  grading,  p.  287.  2.  Give 
practical  suggestions  concerning,  establishing  permanent  bench- 
marks, p.  287;  choosing  the  size  of  squares,  pp.  287  and  432; 
extra  rod  readings;  system  of  marking  corners;  and  of  laying 
out  squares.  3.  Give  the  general  method  of  setting  stakes  for 
grading  land.  p.  287,  §  363.  4.  What  is  the  customary  method 
used  when  the  surface  of  the  ground  is  very  uneven,  making  it 
necessary  to  set  temporary  stakes?  Remark,  p.  288.  5.  Give 
the  general  method  of  setting  stakes,  (a)  for  a  level  grade; 
(b)  for  a  grade  that  slopes  in  one  direction  only;  (c)  for  a  grade 
that  slopes  in  two  directions. 

Note:  If  desired  problems  may  be  given  in  setting  grade  stakes  by  each 
of  the  three  methods  referred  to  in  the  last  question  above. 


Exercise  Lp-6. 
To  Stake  out  a  Vertical  Curve. 

References:    Pages  289-292. 

Equipment:   Level,  leveling  rod,  ax,  and  stakes. 

Directions:  Set  stakes  for  a  vertical  parabola  which  shall 
connect  two  gradients  assigned  by  the  instructor.  Use  the 
method  of  procedure  for  chord  gradients  explained  on  p.  291, 
§  364  (d). 

Field  Notes:  1.  On  the  right-hand  page  make  a  sketch 
similar  to  that  on  p.  290,  giving  the  necessary  data;  give  also 
all  computations  systematically  arranged.  2.  On  the  left-hand 
page  record  all  notes  for  leveling  in  the  usual  form  (see  p.  284), 
giving  the  grade  rods  and  elevations  at  all  points. 

Suggestions:  If  it  is  desired  to  drive  stakes  so  that  their  tops  are  on 
grade,  this  problem  must  be  arranged  by  the  instructor  to  suit  the  nature 
of  the  ground;  e.g.,  a  vertical  curve  of  large  radius  may  be  staked  out  on 
comparatively  level  ground,  using  tall  stakes  for  the  highest  points  on  the 
curve.  The  student  can  then  judge  for  himself  by  the  appearance  of  the 
curve  passing  through  the  tops  of  the  stakes  whether  or  not  the  work  is 
approximately  correct.  If  this  method  is  followed,  however,  the  fact 


68  SPECIAL   PROBLEMS   IN    LEVELING. 

should  be  emphasized .  that  it  is  not  the  usual  method  of  procedure,  but 
that  in  most  cases  each  stake  is  driven,  not  to  grade,  but  with  its  top  a  whole 
number  of  feet  above  or  below  grade  according  to  method  2,  p.  258;  or,  if 
this  is  impracticable,  method  3  is  followed. 

Questions:  1.  Give  two  general  methods  of  finding  elevations 
of  points  on  a  vertical  curve,  p.  289.  2.  If  the  second  method 
is  used,  why  is  the  vertical  scale  usually  much  greater  than  the 
horizontal  scale?  p.  289.  3.  Why  is  the  parabola  more  often 
used  than  the  circle  for  vertical  curves?  p.  289.  4.  Explain 
the  method  of  finding  points  on  a  vertical  parabola  by  tangent 
corrections;  by  successive  chord  gradients,  p.  290.  5.  How 
may  the  elevation  of  any  point  between  stations  be  found? 
p.  290.  6.  Give  two  methods  of  field  work  for  running  in  a 
vertical  curve,  p.  291.  7.  Compare  the  two  methods,  p.  291. 

8.  Explain  how  to  make  the  vertical  parabola  pass  through  a 
point  at  a  given  distance  above  or  below  /.  p.  292,  §  364  (g). 

9.  How  would  you  proceed  when  the  rate  of  change  c  and  the 
two  grades  g  and  g'  are  given?  §  364  (h).     10.  Explain  methods 
of  checking  computations.     Top  and  bottom  of  p.  292;    also 
illustration,  bottom  p.  368. 


GROUP  Co. 

EXERCISES  IN  THE  USE  OF  THE  COMPASS. 


Exercise  Co-1. 
The  Error  of  Sighting  and  Beading  a  Compass. 

References:   Pages  293-295,  p.  101,  §143,  p.  575,  §  575. 

Equipment:   Compass,  tape,  sight-pole,  ax,  and  stakes. 

Directions:  1.  Drive  a  stake  A  and  set  up  the  compass  over 
this  stake.  2.  Drive  a  stake  B  300  or  400  feet  away,  sight  at  a 
pole  held  on  this  stake,  and  read  the  bearing  of  the  line  A  B. 
3.  Move  the  compass  through  an  arc  of,  say,  90°,  thus  changing 
the  reading  of  the  needle;  then,  without  sighting  at  B,  set  the 
compass  at  the  original  bearing  of  AB,  line  in  the  pole  and 
measure  the  distance  this  line  of  sight  passes  to  one  side  or  the 
other  of  the  stake  B.  4.  Repeat  the  work  a  number  of  times, 
changing  the  reading  of  the  needle  and  resetting  the  compass  at 
the  same  bearing  each  time.  From  a  number  of  results  thus 
obtained,  find  the  probable  error  of  sighting  the  compass,  in 
units  of  angular  measure.  (This  will  require  a  rough  measurement 
of  the  distances  from  stake  A  to  stake  5.)  Use  a  form  similar 
to  that  on  p.  19  for  finding  the  probable  error. 

Note :  The  distance  that  the  line  of  sight  passes  to  one  side  or  the  other 
of  the  stake  should  be  entered  in  the  column  headed  "  v."  When  the  prob- 
able error  has  been  obtained  in  units  of  linear  measurement  this  quantity 
divided  by  the  distance  AB  will  give  (approximately)  the  tangent  of  the 
angle  which  corresponds  to  that  probable  error. 

Questions:  1.  Explain  the  method  of  reading  bearings, 
p.  101.  2.  Why  are  the  letters  E  and  W  interchanged  in  the 
compass  box?  p.  102.  3.  What  precaution  should  be  observed 
in  reading  bearings?  4.  Why  is  it  not  advantageous  to  place 
telescopes  on  compasses?  p.  576. 

Note :  Questions  concerning  bearings  asked  in  connection  with  Exercise 
Tr-5,  page  32,  of  this  book  may  be  discussed  in  connection  with  this  exer- 
cise also. 


69 


70      EXERCISES   IN    THE   USE  OF   THE  COMPASS. 

Exercise  Co-3. 
Reading  Bearings. 

References:  Page  101,  §  143;  pp.  111-113;  pp.  541-543; 
p.  575,  §  575. 

Equipment:   Compass,  sight-pole,  ax,  and  stakes. 

Directions:  1.  Set  the  compass  over  a  stake  A.  2.  Drive 
four  stakes,  B,  C,  D,  and  E,  at  random,  each  at  least  200  feet  from 
stake  A,  making  a  four-sided  polygon  BCDE  with  A  in  the 
approximate  center  of  this  polygon.  3.  By  sighting  at  each 
stake  in  succession  read  and  record  the  bearings  of  the  lines 
AB,  AC,  AD,  and  AE.  4.  By  the  method  explained  on  p.  382, 
§  435,  find  the  values  of  the  angles  BAC,  CAD,  DAE,  and  EAB, 
and  compare  their  sum  with  360°. 

Field  Notes:  1.  Make  a  sketch  showing  the  bearing  of  each 
line  and  the  angles  between  lines.  2.  Arrange  the  computations 
for  angles  according  to  the  form  on  p.  383. 

Questions:  1.  What  is  meant  by  the  dip  of  the  needle?  How 
is  this  dip  counteracted?  p.  541.  2.  What  is  meant  by  the 
magnetic  declination  and  the  magnetic  meridian?  p.  541. 
3.  Define  isogonic  lines  and  agonic  line.  p.  543.  4.  What  is 
meant  by  a  west  declination?  an  east  declination?  In  the 
United  States  how  can  you  remember  whether  the  declination 
is  east  or  west  for  any  given  place?  p.  111.  5.  What  is  the 
approximate  magnetic  declination  at  New  York?  at  San  Francisco? 
at  Chicago?  See  Isogonic  chart  opposite  p.  638.  6.  What  is 
meant  by  local  attraction,  and  give  some  of  the  sources  of  such 
attraction,  p.  543.  7.  If  something  about  the  person  deflects 
the  needle,  as,  for  example,  a  knife  or  keys  in  the  pocket,  is  this, 
strictly  speaking,  local  attraction?  p.  543.  8.  Name  five  varia- 
tions of  declination,  p.  541.  9.  Give  some  facts  concerning 
secular  variation,  p.  541.  10.  Give  some  facts  concerning 
diurnal  variation,  p.  542.  11.  Is  annual  variation  the  same  as 
the  change  per  year  in  secular  variation?  p.  543.  12.  To  what 
are  irregular  variations  due?  p.  543.  13.  Describe  various  forms 
of  compasses,  p.  575.  14.  Upon  what  does  the  sensitiveness  of 
the  needle  depend?  p.  575.  15.  What  precautions  should  always 
be  taken  to  avoid  dulling  the  pivot?  p.  294,  §  366  (3).  16.  Give 
the  most  important  requirements  for  a  good  compass,  p.  575. 


EXERCISES   IN  THE   USE   OF   THE  COMPASS.      71 

17.  What  is  the  difference  between  a  plain  compass  and  a  vernier 
compass?  p.  575.  18.  What  is  a  prismatic  compass?  p.  576. 
19.  Describe  three  tests  for  the  compass,  p.  576.  20.  How  may 
a  needle  be  remagnetized?  21.  If  a  compass  is  to  be  put  away 
for  a  considerable  length  of  time,  what  precaution  may  be  taken 
in  order  that  the  needle  may  retain  its  magnetic  strength?  p.  295. 


Exercise  Co-3. 
Compass  Survey  of  a  Polygon. 

References:  Chapter  XXIV,  p.  293;  also  §  566,  p.  541;  §  575, 
p.  575. 

Equipment:  Surveyor's  compass,  chain  or  tape,  sight-poles, 
ax,  and  stakes. 

Directions:  Drive  four  or  five  stakes  at  random,  forming  an 
irregular  polygon  no  side  of  which  is  less  than  150  feet.  Begin- 
ning at  any  stake  survey  this  polygon,  measuring  the  forward 
and  back  bearings  of  each  line  and  its  length. 

Field  Notes:  According  to  Form  9,  p.  297.  (See  Method  of 
Procedure,  p.  298.) 

Suggestion:  If  students  work  in  parties  of  two  each,  one  man  should  run 
the  compass  entirely  around  the  polygon,  and  then  the  problem  may  be 
repeated,  the  other  man  running  the  instrument. 

Questions:  1.  What  bearings  are  usually  kept  in  a  survey? 
p.  113.  2.  In  compass  surveying  why  is  it  well  to  keep  back- 
bearings  also?  p.  295,  §  366  (7).  3.  In  compass  surveying  how 
are  the  relative  positions  of  any  two  points  determined?  p.  293. 

4.  Give  some  objections  to  the  use  of  the  compass,   p.   293. 

5.  What  are  some  of  the  advantages?  p.  293.     6.    Give  some 
practical  suggestions  for  the  use  of  the  compass  concerning  the 
following  points    (see  §  366,  p.  294):     Setting  up;  method  of 
sighting;  method  of  reading  needle;  protecting  the  pivot;  avoid- 
ing sources  of  attraction;  sluggish  needle;   duplicate  readings. 
7.   Which  sight  vane  should  be  next  to  the  eye  in  sighting,  and 
which  end  of  the  needle  should  always  be  read?   p.  294.     8.    Why 
will  reading  the  bearings  at  both  ends  of  a  line  reveal  an  error 
due  to  local  attraction?     9.    When  it  is  impracticable,  because  of 
an  obstruction,  to  take  the  bearing  of  a  line  directly,  how  may  its 
bearing   be   found?    10.  When  is   the   declination   arc   used? 


72      EXERCISES   IN   THE    USE    OF    THE    COMPASS. 

p.  295.     11.   Give  the  general  method  of  making  a  compass 
survey,   p.    295.     12.   How   may   details   be   located?  p.    296. 

13.  If  the  bearings  taken  at  the  two  ends  of  a  line  disagree,  how 
may   it    be    determined   which   is    correct?   p.    296,    §  368  (a). 

14.  Illustrate  how  the  effects  of  local  attraction  may  be  elimi- 
nated from  the  bearings  of  a  number  of  connected  lines,    p.  296. 

15.  What  are  three  chief  sources  of  error  in  compass  surveying? 
p.  298.     16.   What  are  the  limits  of  precision  in  compass  sur- 
veying? p.  298.     17.    Give  the  general  method  of  rerunning  old 
surveys,   p.  298.     18.    If  in  rerunning  boundary  lines  two  points 
on  any  one  line  are  still  preserved,  what  is  the  most  direct  method 
of  ascertaining  the  change  in  magnetic  declination  which  has 
taken  place  since  the  original  survey?   p.  299.     19.    Why  is  it 
important  to  give  on  the  map  of  a  compass  survey  the  date  of 
the    survey?   p.    299.     20.    What    publication    gives    magnetic 
declinations  at  different  places  in  the  United  States?  p.  299. 


OF  THE 

UNIVERSITY  } 

OF 


GROUP  S. 

EXERCISES  IN  THE  USE  OF  THE  STADIA. 

The  exercises  in  this  group  afford  practice  in  measuring  horizontal  dis- 
tances and  in  determining  elevations  by  the  stadia  method. 

Exercise  S-l. 

To  Test  the  Stadia  Interval. 

References:  Pages  300-304. 

Equipment:  Transit  equipped  with  stadia  wires,  stadia  rod, 
steel  tape,  ax,  and  stakes. 

Directions:  Test  the  stadia  interval  for  distances  up  to  400 
feet  according  to  the  method  explained  in  §  374,  p.  302. 

Field  Notes:  Give  the  number  or  the  letter  and  the  maker's 
name  of  the  transit  tested.  Record  the  distance  corresponding 
to  each  reading  of  the  rod,  and  give  the  final  value  of  the  stadia 
interval  as  deduced  from  these  distances. 

Suggestions:  It  is  well  for  several  students  in  the  party  to  test  the  stadia 
interval  for  the  same  transit,  and  the  final  value  of  this  stadia  interval  should 
then  be  deduced  from  the  observations  taken  by  all  of  the  students.  If  the 
stadia  wires  are  adjustable  and  they  are  found  out  of  adjustment,  they 
should  be  reset  as  explained  in  §  375,  p.  303.  This  may  be  done  by  the 
whole  party  working  together  under  the  supervision  of  the  instructor. 

Questions:  1.  Define  stadia,  stadia  wires,  stadia  rod.  p.  300. 
2.  What  are  some  of  the  different  patterns  of  stadia  rods  in 
common  use?  pp.  573  and  574.  3.  Give  some  suggestions  for 
making  a  stadia  rod.  p.  574.  4.  Can  leveling  rods  be  used  as 
stadia  rods?  p.  300.  5.  Define  telemeter;  tachymeter.  p.  300. 
6.  Explain  by  means  of  a  diagram  the  principle  of  the  stadia, 
p.  301.  7.  How  may  the  constant  C  be  determined  by  direct 
measurement?  p.  302.  8.  What  is  the  average  value  of  C  for 
transits?  for  18-inch  wye-levels?  Remark,  p.  302.  9.  Give  the 
general  method  of  testing  stadia  intervals,  p.  302.  10.  Explain 
the  method  of  adjusting  stadia  wires,  p.  303.  11.  Is  it  essential 
that  the  two  stadia  wires  should  be  equally  distant  from  the 
horizontal  cross-wire?  What  advantage  is  there  in  having  them 
equally  distant?  p.  303.  12.  Give  some  practical  suggestions 

73 


74       EXERCISES   IN   THE    USE    OF   THE    STADIA. 

for  adjusting  stadia  wires,  p.  303.  13.  Explain  the  method  of 
graduating  a  rod  for  fixed  stadia  wires,  p.  304.  14.  Explain 
what  is  meant  by  interval  factor,  and  how  it  may  be  ascertained 
in  any  given  case.  p.  304.  15.  Which  is  to  be  preferred  for 
accurate  work  —  adjustable  or  fixed  stadia  wires?  p.  304, 
Practical  Suggestions.  16.  What  effect  has  refraction  in  deter- 
mining the  stadia  interval  (p.  313),  and  when  should  tests  be 
made  for  very  accurate  work  in  graduating  a  rod?  p.  304. 
17.  What  are  the  advantages  of  using  a  standard  rod  and 
correcting  readings  by  an  interval  factor?  p.  304. 


Exercise  S-2. 
To  Measure  Distances  on  Level  Ground  by  the  Stadia. 

References:   Page  304,  §  377;  p.  307,  §  381  (a),  (c),  (d),  (e). 

Equipment:  Transit  with  stadia  wires,  stadia  rod,  tape,  ax, 
and  stakes. 

Directions:  1.  Set  up  the  transit  over  stake  A.  2.  Drive 
four  stakes,  B,  C,  D,  and  E,  at  distances  from  the  transit  varying 
from  about  30  feet  to  300  feet.  3.  Using  the  stadia  method 
only,  find  the  distances  AB,  AC,  AD,  and  AE.  4.  Measure  the 
above  distances  with  the  tape.  5.  Repeat  the  exercises  until  a 
distance  can  be  measured  by  the  stadia  with  reasonable  certainty. 

Field  Notes:  1 .  On  the  right-hand  page  give  a  description  of  the 
work ;  on  the  left-hand  page,  arrange  in  columns  side  by  side  the 
distances  to  each  point  as  found  by  the  stadia  and  as  measured 
with  the  tape.  2.  Give  also  your  conclusions  as  to  the  limit  of 
accuracy  of  the  stadia  method,  basing  your  opinion  upon  the 
results  obtained  in  this  exercise. 

Suggestions:  Four  students  can  work  to  advantage  at  each  transit.  While 
two  are  measuring  by  the  stadia  method,  the  other  two  can  be  measuring 
with  the  tape.  Each  student  should  take  his  turn  in  using  the  transit,  but 
it  is  well  to  use  a  different  set  of  stakes  each  time  to  avoid  being  prejudiced 
by  the  previous  readings. 

Questions:  Give  the  general  method  of  reading  the  stadia  rod. 
p.  304.  2.  What  are  some  of  the  common  mistakes?  p.  305. 

3.  Give  practical  suggestions  for  the  use  of  the  stadia,    p.  307. 

4.  How  accurately  can  distances  be  measured  with  the  stadia? 
p.  307  and  p.  313,  §  386  (a).     5.   How  long  sights  should  be 
taken?  p.  307, 


EXERCISES   IN    THE   USE   OF  THE   STADIA.        75 


Exercise  S-3. 

To  Measure  Horizontal  Distances   on  Sloping  Ground 
by  the  Stadia. 

References:   Pages  305-307. 

Equipment:  Transit  with  stadia  wires,  stadia  rod,  tape,  ax, 
and  stakes. 

Directions:  1.  Set  up  the  transit  over  stake  A  driven  where 
the  ground  is  sloping.  2.  Drive  several  stakes,  B,  C,  D,  E,  at 
distances  from  the  transit  varying  from  30  feet  to  300  feet,  and 
at  points  whose  elevations  vary  considerably.  3.  Read  and 
record  the  inclined  distance  and  the  vertical  angle  to  the  rod  held 
on  each  stake.  4.  Reduce  the  inclined  readings  to  horizontal 
distances  as  explained  on  p.  480,  §  514.  5.  Check  the  results 
by  measuring  horizontal  distances  with  the  tape. 

Field  Notes:  Keep  field  notes  on  the  left-hand  page  according 
to  Form  11,  p.  311,  omitting  the  first  two  columns.  On  the 
right-hand  page,  arrange  in  systematic  form  all  computations  for 
reducing  inclined  distances. 

Suggestions:  1.  It  is  well  to  take  some  of  the  stakes  above  and  some 
below  the  transit.  Oftentimes  the  rod  may  be  held  on  top  of  a  fence,  in  a 
second  or  third  story  window,  or  at  other  points  of  varying  elevations,  instead 
of  on  stakes  driven  in  the  ground.  2.  In  multiplications  for  reducing 
inclined  distances,  use  the  abridged  method,  p.  481.  It  is  well  also  to  use 
reduction  diagrams  and  slide  rules. 

Questions:  1.  By  means  of  a  sketch,  explain  what  two  correc- 
tions are  involved  when  the  line  of  sight  is  inclined?  p.  306. 
2.  Derive  the  formula  for  horizontal  distance,  p.  306.  3.  In 
measuring  horizontal  distances  with  the  stadia,  when  may 
vertical  angles  be  ignored?  Bottom  of  p.  307. 

Exercise  S-4. 

To  Obtain  Vertical  Distances  or  Elevations  by  the 

Stadia. 

Reference:   Page  308. 

Equipment:  Transit  with  stadia  wires,  stadia  rod,  tape,  ax, 
and  stakes. 

Directions:  1 .  Set  up  the  transit  over  the  stake  A  driven  in  slop- 
ing ground.  2.  Drive  stakes  B,  C,  D,  and  E  at  different  eleva- 


76        EXERCISES   IN    THE    USE    OF   THE    STADIA. 

tions,  and  at  distances  from  the  transit  varying  from  50  to  300  feet. 

3.  Find  the  elevation  of  these  stakes  with  respect  to  the  stake 
under  the  transit  by  the  method  explained  in  §  382  (a),  p.  308. 

4.  Repeat  the  work,  finding  the  elevations  of  the  same  stakes 
with  respect  to  a  near-by  bench-mark.     5.    Find   the  elevation 
of  each  stake  with  respect  to  the  stake  under  the  transit,  by 
the  first  method  explained  in  §  341,  p.  264,  using  the  tape  for 
measuring    horizontal    distances.     Compare    the    results    thus 
obtained  with  corresponding  elevations  obtained  by  the  stadia 
(step  3,  above). 

Field  Notes:  1.  On  the  left-hand  page  keep  the  field  notes  ac- 
cording to  Form  12,  p.  311,  omitting  the  second  column.  2.  On 
the  right-hand  page,  keep  in  a  systematic  form  all  computations. 
3.  Show  side  by  side  the  elevations  as  obtained  from  step  3  and 
step  5. 

Suggestions:  1.  See  suggestions  of  the  preceding  problem.  2.  When 
vertical  distances  or  elevations  are  involved,  it  is  essential  that  the  algebraic 
sign  of  the  vertical  angle  should  be  carefully  entered  in  the  notes. 

Questions:  1.  Explain  the  method  of  obtaining  elevations  of 
points  with  reference  to  a  point  under  or  near  the  instrument 
(p.  308,  §  382  (a));  with  reference  to  a  bench-mark,  some  dis- 
tance from  the  instrument.  §  382  (b).  2.  What  is  one  of  the 
first  things  to  be  given  definitely  in  the  notes?  §  382  (c).  3.  Upon 
what  does  the  accuracy  of  elevations  depend?  §  382  (d).  4.  If 
an  error  as  large  as  6'  is  made  in  a  vertical  angle  of  about  14°, 
what  would  be  the  resulting  error  in  elevation  at  a  point  200 
feet  from  the  transit?  p.  309.  5.  If  a  vertical  angle  of  about 
14°  is  measured  correctly,  but  the  distance  as  obtained  by  the 
stadia  is  1  foot  greater  than  or  1  foot  less  than  it  should  be, 
what  is  the  resulting  error  in  elevation?  p.  309.  6.  Is  an  error 
in  measuring  a  vertical  angle  more  important  in  large  angles 
than  in  small  angles,  or  vice  versa?  p.  309.  7.  Is  an  error  in 
measuring  distances  more  important  when  the  vertical  angle  is 
large,  or  when  it  is  small?  p.  309.  8.  In  ordinary  work,  how 
closely  should  distances  and  vertical  angles  be  measured?  p.  309. 
9.  When  may  vertical  angles  be  read  without  the  use  of  the 
vernier,  and  how  closely  should  the  corresponding  distances  be 
read?  p.  309. 


EXERCISES    IN   THE    USE   OF    THE    STADIA.       77 

Exercise  S-5. 

Stadia  Survey  of  a  Polygon.      (Azimuth  Method.) 

References:  Pages  309-317. 

Equipment:  Transit  with  stadia  wires,  stadia  rod,  ax,  and 
stakes. 

Directions:  1.  Drive  four  stakes  to  serve  as  four  corners  of 
an  irregular  polygon  the  sides  of  which  vary  in  length  from  less 
than  100  feet  to  more  than  200  feet.  2.  Survey  this  polygon  by 
the  first  azimuth  method  (p.  121),  using  the  stadia  for  measuring 
all  distances.  Assume  a  magnetic  north  and  south  line  as  a 
reference  meridian.  Find  the  elevations  of  all  stakes  with 
reference  to  a  bench-mark  near  the  first  station  by  the  method 
explained  on  p.  308. 

Field  Notes:   Use  Form  10,  p.  310. 

Suggestions:  Follow  the  practical  suggestions  given  at  the  bottom  of 
p.  309.  Two  men  can  work  to  advantage  in  each  party  in  this  exercise.  If 
time  permits,  one  should  run  the  transit  entirely  round  the  polygon,  the  other 
acting  as  rodman.  Then  the  exercise  should  be  repeated,  the  two  men  inter- 
changing positions  and  going  round  the  polygon  in  the  opposite  direction. 
If  desired,  one  of  the  other  methods  for  running  transit  lines  may  be  used 
instead  of  the  azimuth  method,  or  additional  exercises  may  be  given  similar 
to  this,  involving  the  other  methods  of  running  transit  lines. 

Questions:  1.  What  methods  are  used  for  running  transit 
lines  in  stadia  surveys?  p.  309.  2.  What  methods  are  used  for 
locating  details?  p.  309.  3.  Give  some  practical  suggestions 
pertinent  to  stadia  surveying.  4.  Compare  the  forms  of  notes 
given  on  pp.  310  and  311.  5.  Give  some  of  the  sources  of  error 
in  stadia  surveying,  p.  312.  6.  Explain  why  it  is  unwise 
during  midday  hours  to  take  sights  which  require  the  line  of 
sight  to  pass  nearer  than  three  feet  to  the  ground,  p.  313. 
7.  What  should  be  the  maximum  probable  error  of  sighting  for 
distances  up  to  100  feet?  p.  313.  8.  What  may  be  expected  as 
a  mean  discrepancy  between  measurements  made  by  the  stadia 
and  by  the  tape  for  distances  of  approximately  300  feet?  p.  314. 

9.  What  is  the  maximum  error  likely  to  occur  in  ordinary  work 
in  finding  the  elevation  of  a  point  from  a  vertical   angle  of 
about  10°  and  the  length  of  sight  of  about  300  feet?  p.  314. 

10.  Give  the  formula  for  determining  the  maximum  allowable 
error  in  the  sum  of  the  lengths  of  the  lines  traversed,  p.  315. 


78        EXEBCISES    IN    THE    USE    OF    THE    STADIA. 

11.  Give  practical  suggestions  for  stadia  surveying  concerning 
the  following  points:  The  constant;  the  stadia  wires;  method 
of  sighting;  reading  the  rod;  length  of  sight;  method  of  sighting 
when  two  stations  are  too  far  apart  for  a  single  sight;  method 
followed  when  only  a  small  portion  of  the  rod  can  be  seen ;  when 
vertical  angles  should  be  taken  into  account ;  checking  distances 
between  stations;  checking  distances  of  side  shots;  method  of 
determining  elevations;  point  of  reference  for  elevations;  the 
relations  between  the  length  of  sights  and  the  vertical  angle; 
effect  of  an  error  in  the  adjustment  of  the  telescope  level-bubble 
avoiding  needless  refinements. 


GROUP   P. 

EXERCISES   IN  THE   USE  OF  THE  PLANE  TABLE. 

The  first  five  exercises  in  this  group  afford  practice  in  the  five  fundamental 
methods  used  in  plane-table  surveying.  The  last  exercise  is  one  on  the 
"  three-point  problem." 

Exercise  P-l. 
Plane-table  Survey  of  a  Polygon. 

(Method  of  Radiation.) 

References:   Pages  318-322;  also  pages  576,  577. 

Equipment:  Plane-table,  and  accessories  (scale,  hard  pencil, 
pencil  sharpener,  drawing  paper,  triangles,  fine  needle,  thumb 
tacks),  steel  tape,  ax,  and  stakes. 

Directions:  Drive  four  stakes  at  random  so  that  each  will  be 
the  corner  of  a  polygon,  no  side  of  which  is  less  than  150  feet  in 
length.  2.  Set  up  the  plane-table  near  the  center  of  this 
polygon,  and  locate  the  corners  by  the  method  of  radiation, 
p.  321.  3.  Scale  the  lengths  of  the  sides  of  the  polygon  and 
mark  these  lengths  on  the  map;  measure  the  lengths  of  the 
sides  with  the  tape  and  mark  these  lengths  on  the  map,  thus 
affording  a  comparison  and  a  check. 

Suggestions:  In  this  exercise  adopt  as  large  a  scale  as  practicable  and 
have  the  polygon  come  within  the  limits  of  the  board. 

Questions:  1.  Give  some  of  the  requirements  for  the  board  of 
a  plane-table,  p.  576;  for  the  alidade,  p.  577.  2.  What  are 
some  of  the  accessories?  p.  577.  3.  What  is  a  traverse  board? 
p.  577.  4.  Give  some  of  the  tests  for  the  plane-table,  p.  577. 
5.  What  is  the  peculiar  characteristic  of  plane-table  surveying? 
p.  318.  6.  How  are  linear  measurements  made?  p.  318. 
7.  For  what  kind  of  work  is  the  plane-table  especially  useful? 
p.  -318.  8.  Give  some  of  the  advantages  of  the  plane-table, 
p.  319.  9.  Some  of  the  disadvantages,  p.  319.  10.  Give 
some  suggestions  for  setting  up  the  plane-table,  p.  319.  11.  In 
most  plane-table  work  is  it  essential  to  get  a  point  on  the 
map  representing  the  position  of  the  plane-table  exactly  over 
the  corresponding  point  on  the  ground?  p.  320.  12.  Explain 
the  method  of  radiation  (p.  321).  13.  What  is  the  chief  use  of 

this  method?  p.  322. 

79 


80    EXERCISES   IN   THE   USE   OF   THE   PLANE   TABLE. 

Exercise  P-2. 
Plane-table   Surveying  of  a  Polygon. 

(Method  of  Progression,  or  Traversing.) 

Reference:   Page  322. 

Equipment:   Same  as  for  the  preceding  exercise. 

Directions:  1.  Repeat  the  preceding  exercise,  using  the 
method  of  progression,  or  traversing,  p.  322.  2.  Check  the 
work  by  measuring  the  diagonals  of  the  polygon  and  comparing 
the  results  with  the  lengths  obtained  by  scaling  the  map. 

Suggestions:  1.  Adopt  a  scale  as  large  as  the  limits  of  the  board  will 
permit.  2.  Throughout  the  work  the  first  sight  after  orienting  the  table 
should  be  a  check  sight.  These  check  sights  are  very  important  and 
should  never  be  omitted. 

Questions:  1.  Explain  the  method  of  orienting  the  plane 
table,  p.  322.  2.  To  which  method  of  transit  surveying  does 
this  method  correspond?  p.  323.  3.  How  should  check  sights 
be  taken?  p.  323.  4.  Is  it  necessary  to  set  up  over  the  last 
station?  p.  323.  5.  If  it  is  impracticable  to  set  up  over  bound- 
ary lines,  how  would  you  proceed?  p.  323.  6.  How  can  a 
four-sided  polygon  be  plotted  in  two  set-ups,  and  how  could 
the  positions  of  the  corners  be  checked?  p.  323.  7.  Can  the 
method  of  traversing  be  used  if  some  of  the  stations  are  inac- 
cessible? p.  323.  8.  For  what  kind  of  work  is  the  method 
ordinarily  used?  p.  323.  9.  In  locating  roads,  banks  of 
streams,  etc.,  where  should  the  stations  be  chosen?  p.  323. 
10.  How  may  details  of  a  plane-table  survey  be  located? 
p.  323.  11.  In  a  large  topographic  survey  how  are  primary 
stations  a  valuable  check  on  plane-table  work?  p.  323. 

Exercise  P-3. 
Plane-table  Survey  of  a  Polygon. 

(Method  of  Radio-Progression.) 

Reference:  Page  323. 

Equipment:  The  same  as  for  Exercise  P-l. 

Directions:  Repeat  Exercise  P-l,  using  the  method  of  radio- 
progression. 

Questions:  1.  Give  some  practical  suggestions  for  this 
method,  p.  324.  2.  Comment  on  this  method,  p.  324. 


EXEECISES   IN   THE   USE   OF   THE   PLANE   TABLE.    81 

Exercise  P-4. 
Plane-table  Survey  of  a  Polygon. 

(Method  of  Intersection.) 

Reference:   Page  325. 

Equipment:   Same  as  for  Exercise  P-l. 

Directions:  Repeat  Exercise  P-l,  using  the  method  of  inter- 
section, p.  325.  Although  the  four  stations  may  be  located 
with  two  set-ups,  the  work  should  be  checked  by  setting  up  at  a 
third  station. 

Questions:  1.  Give  practical  suggestions  concerning  choice 
of  stations;  method  of  check  lines,  p.  325.  2.  What  are  the 
advantages  of  this  method,  and  in  what  kind  of  work  is  it 
especially  useful?  p.  326. 

Exercise  P-5. 
Plane-table  Survey  of  a  Polygon. 

(Method  of  Resection.) 

Reference:    Page  326. 

Equipment:   Same  as  for  Exercise  P-l. 

Directions:  Repeat  Exercise  P-l,  using  the  method  of  resection, 
p.  326. 

Questions:  1.  What  is  the  peculiar  characteristic  of  this 
method?  p.  326.  2.  Give  practical  suggestions  concerning  the 
method  of  setting  up;  method  of  proceeding  when  there  are 
more  than  four  sides ;  method  of  check  sights.  3.  When  is  this 
method  used?  p.  327.  4.  What  are  special  cases  of  this 
method?  p.  327. 

Exercise  P-6. 
Discussion  of  Plane-table  Surveying. 

(Exercise  for  the  Classroom.) 

1.  Compare  the  five  methods  used  in  plane-table  surveying, 
p.  327.  2.  Give  practical  suggestions  concerning  selection  of 
paper;  method  of  carrying  paper;  fastening  paper  to  board; 
protecting  paper  in  case  of  rain;  connecting  different  sheets 
when  two  or  more  are  used.  p.  327.  3.  Give  practical  sug- 


82   EXERCISES   IN   THE   USE   OF   THE   PLANE   TABLE. 

gestions  for  manipulation  of  the  plane-table,  including,  turning 
it  slowly;  manipulating  the  alidade;  disturbance  of  the  board, 
p.  327.  4.  Give  practical  suggestions  for  plotting,  including, 
method  of  sharpening  pencil;  use  of  scale;  drawing  lines; 
locating  several  points  on  the  same  straight  line;  drawing  lines 
close  to  a  straight  edge;  keeping  track  of  points  and  lines. 
p.  328.  5.  Give  general  suggestions  including  use  of  colored 
glasses;  rules  for  cleanliness;  drawing  a  north  and  south 
meridian;  the  use  of  check  sights,  p.  328.  6.  How  are  verti- 
cal angles  measured,  and  in  what  kind  of  work  are  they  most 
used?  p.  328.  7.  Discuss  practical  questions  relating  to  field 
work,  including,  three  suggestions  for  choice  of  scale;  choice  of 
stations;  method  of  locating  details;  limits  of  error;  sources  of 
error,  p.  328. 


Exercise  P-7. 
Plane-table  Practice  in  the  Three-point  Problem. 

Reference:  Pages  329-334. 

Equipment:  Plane-table  and  accessories,  three  sight  poles, 
piece  of  tracing  cloth  or  tracing  paper. 

Directions:  1.  Choose  three  points,  A,  B  and  C,  visible  from 
a  station  P  to  be  occupied  by  a  plane-table.  The  points  a,  b, 
and  c  should  be  plotted  to  represent  three  visible  points. 

2.  Find  the  point  p  corresponding  to   P  by  the  mechanical 
solution  on  p.  329.     3.    Check  the  work  by  the  graphic  solution 
(Bessel's  method),  p.  330.     4.    Repeat  the  exercise  by  the  trial 
method  (Coast  Survey  method),  p.  332. 

Suggestions:  In  this  exercise  time  may  be  saved  if  the  three  given  points 
are  plotted  before  going  into  the  field.  For  this  reason  the  polygon  used 
in  one  of  the  plane-table  exercises  already  given  may  be  chosen  for  this 
work,  and  three  of  its  corners  transferred  to  a  clean  sheet  of  paper  by 
pricking  through.  When  the  fourth  corner  has  been  determined  by  the 
three-point  method,  the  map  of  the  whole  polygon  may  be  compared  with 
maps  made  by  other  methods.  Of  course,  it  should  be  pointed  out  that 
when  the  three-point  problem  occurs  in  practice  the  three  points  them- 
selves are  usually  long  distances  apart. 

Questions:  1.  Explain  the  mechanical  solution  of  the  three- 
point  problem,  p.  329.  2.  Comment  on  this  method,  p.  330. 

3.  Explain    Bessel's    method,  p.    330.     4.    What    is    the    chief 
objection  to  Bessel's  method?  p.  330.     5.    How  may  this  diffi- 


EXERCISES   IN    THE   USE   OF   THE   PLANE   TABLE.    83 

culty  be  overcome?  p.  330.  6.  On  what  principle  is  Bessel's 
solution  based?  p.  331.  7.  Explain  Llano's  method,  p.  331. 
8.  Explain  the  Coast  Survey  method,  p.  332.  9.  Give  rules 
for  guidance  in  Coast  Survey  method,  p.  332.  10.  Explain 
the  Two-point  Problem,  p.  334. 


GROUP  To. 

EXERCISES  IN  TOPOGRAPHIC  SURVEYING. 

The  exercises  in  this  group  afford  practice  in  practically  all  of  the  methods 
for  locating  contours  that  are  commonly  used  in  topographic  surveying. 

Exercise  To-1. 
Running  in  a  Contour. 

References:   Pages  337-341. 

Equipment:   Transit,  leveling  rod,  ax,  and  stakes. 

Directions:  1.  Choose  a  place  on  a  side  hill  where  the  surface 
is  quite  irregular;  set  up  a  transit  and  clamp  the  telescope  so  that 
the  line  of  sight  is  horizontal.  2.  Using  the  transit  as  a  level, 
backsight  on  some  near-by  bench-mark,  thus  obtaining  the 
elevation  of  the  line  of  sight.  3.  Setting  the  target  at  the  proper 
grade  rod,  find  points  at  intervals  of  about  25  feet  on  a  contour 
whose  elevation  is  an  even  multiple  of  5  feet,  marking  each  point 
with  a  stake. 

Suggestion:  In  this  exercise  the  elevation  of  the  contour  is  immaterial, 
the  object  being  to  set  a  row  of  stakes  200  or  300  feet  long  that  will  show 
to  a  student  how  a  given  contour  winds  in  and  out  along  the  surface  of  the 
ground  (see  also  Suggestion,  p.  337). 

Questions:   1.    Define    contour;     contour    interval.       p.    337. 

2.  What  are  some  of  the  customary  contour  intervals?   p.  337. 

3.  How  can  the  imagination  be  helped  in  tracing  a  contour  with 
the  eye?   p.  337.     4.   What  is  a  topographic  map?     What  is  its 
advantage  over  an  ordinary  map?  p.  337.     5.    How  would  the 
surface  of  a  perfect  cone  be  represented  by  contours?  p.  338. 

6.  Give   some   of  the   fundamental   principles   concerning  the 
following  points :     Contour  lines  crossing;  contour  lines  merging ; 
contour  lines  near  together  or  far  apart ;  line  of  steepest  slope  at 
any  point;  difference  between  closed  contour  lines  indicating  a 
hill  and  similar  lines  indicating  a  depression ;  continuity  of  contour 
lines;  contour  lines  in  pairs;  a  single  contour  line  between  two 
higher  or  two  lower  lines;  contour  lines  across  a  stream,   p.  338. 

7.  Why   cannot   a   contour   line    turn   down   stream?   p.    338. 

84 


EXERCISES   IN   TOPOGRAPHIC    SURVEYING.        85 

8.  Define  ridge  line;  valley  line.  p.  339.  9.  Where  do  the 
sharpest  bends  or  curves  in  a  contour  line  occur?  p.  339. 
10.  When  the  convex  side  of  the  curve  is  toward  lower  ground, 
does  it  indicate  a  ridge,  or  a  valley?  p.  339.  11.  What  two 
general  methods  are  there  of  locating  contours?  p.  340. 
12.  Explain  the  modified  method,  p.  341.  13.  In  the  modified 
method,  what  should  be  the  size  of  square?  p.  341.  14.  Give  a 
system  of  numbering  the  corners  of  squares,  p.  341. 


Exercise  To-3. 

Topographic  Survey  of  a  Small  Area. 

(Direct  Method  of  Running  in  Contours  with  a 

Spirit  Level.) 

References:   Pages  348,  §  411  (a);  339,  §  401;  341-348. 

Equipment:  Transit,  level,  leveling  rod,  drawing-board  mounted 
on  a  tripod  with  accessories  for  plotting,  including  protractor, 
scale,  and  triangles. 

Directions:  Choose  a  place  where  the  surface  of  the  ground 
is  quite  irregular,  and  make  a  topographic  survey  of  a  small  tract 
a  few  hundred  feet  square  by  the  method  explained  in  the  first 
illustration,  p.  348,  §  411  (a). 

Suggestions:  1.  Each  member  of  the  party  should  follow  the  method  of 
procedure  for  his  position,  outlined  on  p.  349,  and  before  the  survey  is 
completed  each  should  have  had  practice  in  all  of  the  different  positions. 
Read  also  Remark,  p.  348.  2.  After  each  member  of  the  party  has  had 
practice  in  plotting  notes  in  the  field,  it  may  be  well  to  continue  the  survey 
without  plotting  the  notes,  using  the  combination  method  for  field  notes 
explained  on  p.  346. 

Questions:  1.  Give  the  general  method  of  procedure  for  the 
levelman.  p.  349.  2.  As  a  rule,  is  it  better  to  carry  the  work  of 
leveling  from  station  to  station  as  the  work  progresses,  or  first 
to  run  a  line  of  levels  establishing  bench-marks,  and  then  to 
start  anew  from  each  station  in  running  in  contours?  p.  349. 

3.  Give   the   method   of  procedure   for  the    rodman.    p.    349. 

4.  Give  the  method  of  checking  a  grade  rod.    p.  349.     5.    How 
close  should  the  line  of  sight  come  to  the  center  of  the  target? 
p.  349.     6.   Give  the  method  of  procedure  for  the  transit  man. 
p.  349.     7.   Give  the  method  of  orienting  the  transit.     8.   Give 


86       EXERCISES   IN   TOPOGBAPHIC    SURVEYING. 

the  method  of  procedure  for  the  azimuth  method,  p.  156.  9.  Is 
it  usually  necessary  to  read  the  vernier  for  either  vertical  or  hori- 
zontal angles?  p.  349,  p.  109,  §  152  (d).  10.  When  may  vertical 
angles  be  ignored?  p.  307.  11.  What  distances  should  be  read 
twice?  p.  349.  12.  What  lines  should  be  checked  with  a  needle? 
p.  349.  13.  Give  the  method  of  procedure  for  the  draftsman, 
p.  349.  14.  Give  two  methods  of  plotting  azimuths,  p.  349. 
15.  Give  different  methods  of  reducing  inclined  stadia  read- 
ings, pp.  480-483.  16.  Give  a  method  of  keeping  track  of 
points,  p.  349. 

Exercise  To-3. 

Topographic  Survey  of  a  Small  Area. 
(Contours  Interpolated  by  Spirit  Leveling.) 

References:   Page  340,  §  402  (b);  p.  350,  §  411  (b). 

Equipment:   Same  as  for  the  preceding  exercise. 

Directions:  Make  a  topographic  survey  of  a  small  area  as  in 
the  preceding  exercise,  but  use  the  method  explained  in  the 
second  illustration  on  p.  350. 

Suggestions:  1,  See  suggestions  for  preceding  exercise.  2.  It  may  be 
well  to  cover  exactly  the  same  ground  as  in  the  preceding  exercise,  and  to 
compare  the  map  obtained  by  interpolating  contours  with  that  obtained  in 
the  preceding  exercise  by  running  in  contours. 

Exercise  To-4. 

Topographic  Survey  of  a  Small  Area. 

(Contours  Interpolated  by  Means  of  the  Vertical  Angle 

Method.) 

Reference:  Page  350,  §  411  (c). 

Equipment:  Transit,  stadia  rod  or  leveling  rod,  drawing-board 
mounted  on  tripod  with  accessories  for  plotting,  including  pro- 
tractor, scale,  and  triangles. 

Directions:  Make  a  topographic  survey  of  a  small  area  as  in 
the  preceding  exercise,  but  use  the  vertical  angle  and  stadia  for 
determining  elevations  instead  of  the  spirit  level,  following  the 
method  of  procedure  outlined  in  the  third  illustration,  p.  350. 

Suggestions:   See  suggestions  for  the  preceding  exercise. 


EXERCISES   IN   TOPOGRAPHIC    SURVEYING.        87 

Questions:  1.  Give  the  method  of  procedure  for  the  transit- 
man,  p.  350.  2.  How  can  spirit  leveling  be  used  in  connection 
with  this  method?  p.  350.  3.  Give  the  method  of  procedure 
for  the  rodman.  p.  350.  4.  Give  the  method  of  procedure  for 
the  computer,  p.  350.  5.  Explain  the  use  of  the  abridged 
method  of  multiplication  in  reducing  stadia  readings,  p.  481. 

6.  Give  the  method  of  procedure  for  the  draftsman,    p.  350. 

7.  Give  precautions  for  keeping  track  of  points,   p.  350. 


Exercise  To-5. 

Questions  Pertaining  to  Topographic  Surveying. 
(For  Class-room  Discussion.) 

Questions:  I.  Name  the  different  kinds  of  work  done  in  a 
topographic  survey,  p.  339.  2.  What  is  meant  by  horizontal 
control?  p.  339.  3.  What  is  meant  by  vertical  control?  p.  339. 
4.  Is  the  work  of  horizontal  control  always  carried  on  simul- 
taneously with  that  of  vertical  control?  p.  339.  5.  Give  the 
different  methods  of  establishing  points  of  horizontal  control, 
p.  340.  6.  Give  the  different  methods  of  establishing  points  of 
vertical  control,  p.  340. 

Questions  Concerning  Horizontal  Control. 

7.   Method  of  establishing  primary  stations  in  an  extensive  sur- 
vey?  p.  341.     8.    Method   of   establishing   secondary   stations? 

9.  Method  of  tying  the  survey  to  a  reference  meridian?   p.  341. 

10.  Methods  of  locating  details?  p.  342.     11.    General  methods 
of  locating  contours?   p.  342.     12.   For  angular  measurements, 
is  the  azimuth  or  the  direct  angle  method  most  used,  and  why? 
p.  342.     13.   What  three  other  methods  of  horizontal  control  are 
frequently  used?  p.  342.     14.   What  method  is  most  useful  for 
linear   measurements   in    a   topographic    survey?   p.    342.     15. 
What  precautions  should  be  taken  when  the  azimuth  method  is 
used?  p.  342.     16.   What  precaution  should  be  taken  in  estab- 
lishing sub-stations?  p.  342.     17.   As  a  rule,  is  it  necessary  to 
read  the  vernier  in  locating  contour  points?     Give  an  illustration 
of  the  error  involved  in  not  reading  the  vernier,  p.  343. 


88       EXERCISES   IN   TOPOGRAPHIC    SURVEYING. 

Questions  Concerning  Vertical  Control. 

18.  Methods  of  determining  elevations  of  primary  stations? 
p.  343.  19.  Methods  of  determining  elevations  of  secondary 
stations?  p.  343.  20.  Methods  of  determining  elevations  of 
contour  points?  p.  343.  21.  In  reading  vertical  angles  to 
contour  points,  is  it  necessary  to  read  the  vernier?  Illustrate 
the  error  involved  in  not  reading  the  vernier,  p.  343. 

General  Questions  of  Field  Work. 

22.  Give  some  considerations  which  govern  the  choice  of  stations 
for  horizontal  control:  (a)  for  triangulation  stations,  p.  192, 
§  247;  (b)  for  secondary  stations,  p.  149,  §  216.  23.  In  general, 
from  what  stations  are  contours  most  easily  controlled?  p.  344. 
24.  What  are  some  of  the  other  places  where  stations  should  be 
located?  p.  344.  25.  Give  some  suggestions  for  choosing  stations 
for  vertical  control,  p.  344.  26.  Give  suggestions  for  choosing 
controlling  points  of  contours,  p.  344.  27.  Give  additional 
suggestions  for  choosing  controlling  points  for  contours  when  the 
method  of  interpolation  is  used.  p.  344.  28.  What  considera- 
tions govern  the  choice  of  contour  intervals?  29.  Give  some  of 
the  considerations  which  govern  the  choice  of  methods  and  of 
instruments,  p.  345.  30.  Give  some  of  the  common  combina- 
tions of  instruments  and  methods,  p.  346. 

Questions  Concerning  Field  Notes. 

31.  Give  two  general  methods  of  keeping  field  notes  in  topo- 
graphic surveying,  p.  346.  32.  Explain  the  combination 
method  of  keeping  field  notes,  p.  346.  33.  Explain  the 
method  of  plotting  notes  in  the  field,  p.  347.  34.  Give  some 
suggestions  for  sketching  topography,  p.  347.  35.  Give  some 
practical  suggestions  for  field  notes  concerning  the  following 
points  (347):  special  form  of  note  book;  common  mistake  in 
recording;  uses  of  drawing-board  and  protractor;  keeping  track 
of  the  points;  effect  of  moisture  on  paper;  choice  of  scale. 


GROUP   M. 

EXERCISES  IN  DETERMINING  A  TRUE  MERIDIAN. 

The  exercises  in  this  group  afford  practice  in  the  determination  of  a  true 
meridian  both  by  observations  on  Polaris  and  by  observations  on  the  sun. 

Exercise  M-l. 

Determination  of  a  Meridian  by  Observations  on  Polaris 
at  Elongation. 

Reference:  Chapter  XXVIII,  p.  354. 

Equipment:  Transit,  lanterns,  ax,  stakes. 

Directions:  1.  Before  the  night  of  the  observation,  look  up  the 
time  of  elongation  of  Polaris.  2.  Set  up  over  a  stake  and  pro- 
ceed as  explained  in  §  414,  p.  356. 

Field  Notes:  Keep  a  complete  record  of  the  work  done,  includ- 
ing a  sketch  showing  the  position  of  all  stations  or  stakes. 

Suggestions:  It  is  well  to  conduct  this  exercise  in  connection  with  some 
regular  survey.  In  that  case,  on  some  day  previous  to  the  night  of  obser- 
vation, set  a  number  of  stakes,  one  for  each  party,  on  one  of  the  main  transit 
lines  of  the  survey.  The  stakes  should  be  at  least  twenty  feet  apart  and 
in  such  a  place  that  when  the  telescope  is  depressed  after  sighting  at  Polaris, 
a  clear  sight  may  be  had  from  each  stake  for  at  least  300  feet.  If  this  is 
done  the  true  azimuth  or  the  true  bearing  of  the  transit  line  may  be  com- 
puted the  day  following  the  observation  by  measuring  the  angle  between 
each  line  established  at  the  time  of  the  observation  and  the  transit  line 
itself.  (See  sketch,  p.  390.)  The  results  thus  obtained  by  different  parties 
may  then  be  compared. 

Adjustments  of  the  transit  should  be  tested  previous  to  the  observation. 
It  is  well,  however,  to  follow  the  modified  method  explained  in  §  414  (a), 
p.  357,  thus  eliminating  error  due  to  adjustment.  Each  party  should  be 
able  to  take  several  pairs  of  observations,  checking  those  which  are  taken 
more  than  10  minutes  before  or  after  elongation  by  the  approximate  formula 
on  p.  359. 

Questions  concerning  Polaris:  1.  Is  Polaris  exactly  at  the 
north  pole?  p.  354.  2.  If  any  star  were  at  the  pole  how  would  a 
true  meridian  be  determined?  p.  354.  3.  Why  is  Polaris  chosen 
for  observations?  p.  354.  4.  Describe  a  simple  way  of  finding 
Polaris,  p.  355.  5.  To  what  constellation  does  Polaris  belong? 
p.  355.  6.  Define  upper  culmination  and  lower  culmination, 
p.  355.  7.  Define  eastern  elongation  and  western  elongation,  p.  355. 

89 


90    EXERCISES  IN  DETERMINING  A  TRUE  MERIDIAN. 

8.  What  is  the  sidereal  day?  p.  355.  9.  If  Polaris  reaches 
its  eastern  elongation  (or  any  other  point  in  its  orbit)  at 
7.45  P.M.  on  one  evening,  at  what  time  will  it  reach  the  same  point 
on  the  next  evening?  p.  355.  10.  Define  polar  distance.  What 
is  its  approximate  value  and  approximate  rate  of  change  per  year? 
p.  355.  11.  If  an  observer  at  the  equator  points  the  telescope 
of  his  transit  at  Polaris  when  at  its  eastern  elongation,  how  far 
will  the  line  of  sight  be  east  of  the  true  north?  p.  355.  12.  Ex- 
plain why  as  the  observer  moves  north  from  the  equator  the  angle 
between  a  line  of  sight  to  Polaris  at  elongation  and  the  true 
meridian  grows  larger,  p.  355.  13.  Explain  the  difference  between 
azimuth  and  polar  distance,  p.  355.  14.  How  can  one  tell  at 
what  vertical  angle  to  set  the  telescope  in  order  to  bring  Polaris 
into  the  field?  p.  356.  15.  When  Polaris  is  at  its  upper  or  lower 
culmination,  how  can  the  meridian  be  obtained?  p.  356.  16. 
What  is  an  approximate  method  of  determining  when  Polaris 
reaches  its  culmination?  p.  356.  17.  When  Polaris  is  between 
elongation  and  culmination,  how  can  its  azimuth  be  determined? 

Questions  concerning  the  methods  of  observing  Polaris:  18. 
Name  three  methods  of  observing  Polaris,  p.  356.  19.  Give  in 
order  the  steps  which  must  be  taken  in  observing  Polaris  at  elon- 
gation, p.  356.  20.  What  two  objections  are  there  to  taking 
only  one  observation  of  Polaris  at  elongation?  p.  357.  21.  Ex- 
plain a  modified  method  by  which  these  objections  may  be 
overcome,  p. 357.  22.  Explain  how  to  calculate  the  time  of  elong- 
ation, p.  357.  23.  Why  is  it  necessary  that  the  transit  should 
be  in  adjustment  and  that  special  pains  should  be  taken  in 
leveling  up?  p.  357.  24.  What  is  a  common  way  of  bringing 
Polaris  into  the  field  of  the  telescope?  p.  357.  25.  Give  practical 
suggestions  for  focusing;  for  illuminating  cross-hairs,  p.  357. 
26.  Describe  the  movement  of  Polaris  in  respect  to  cross-hairs  as 
the  star  approaches  elongation,  p.  357.  27.  What  precaution 
should  be  taken  after  sighting  on  a  star  before  depressing  the 
telescope?  p.  358.  28.  Give  practical  suggestions  for  setting  a 
stake  and  establishing  the  point  after  depressing  the  telescope, 
p.  358.  29.  Explain  the  use  of  the  approximate  formula  for  check- 
ing observations,  p.  358. 

Questions  concerning  other  methods  of  observing  Polaris:  30. 
Explain  the  method  of  observing  at  culmination,  p.  358.  31. 
Explain  the  method  of  observing  Polaris  at  any  time.  p.  358. 
32.  What  are  the  advantages  of  observing  Polaris  at  elongation? 


EXBBCISBS  IN  DETERMINING  A  TRUE  MERIDIAN.    91 

p.  358.  33.  What  is  the  largest  permissible  error  if  this  method 
is  used?  p.  358.  34.  What  are  the  advantages  and  disadvan- 
tages of  the  method  at  culmination;  at  any  time?  p.  358.  35.  Ex- 
plain how  a  true  meridian  may  be  determined  roughly  by  means 
of  a  plumb-line,  p.  358.  36.  What  error  may  be  expected  in  this 
method?  p.  358.  37.  Explain  the  method  of  determining  mag- 
netic declination,  p.  358.  38.  Give  practical  suggestions  concern- 
ing the  declination  arc;  overcoming  a  lack  of  sensitiveness  of  the 
needle;  determining  the  declination  without  staking  out  a  north 
and  south  line. 

Exercise  M-2. 

Determination  of  a  Meridian  by  a  Single  Observation 
on  the  Sun. 

References:  Appendix,  pp.  620-627. 

Equipment:  Transit,  stakes,  ax. 

Directions:  Set  up  at  one  end  of  a  line  the  bearing  of  which  is 
to  be  determined,  and  follow  the  directions  given  in  Art.  603, 
pp.  624  and  625. 

Field  Notes:  For  form  see  Art.  603  (d),  p.  627. 

Suggestions:  (Read  also  the  practical  suggestions  on  p.  625,  noting  par- 
ticularly suggestion  (3)  as  to  leveling  up,  also  suggestion  (15),  p.  88.)  The 
transit  should  be  in  perfect  adjustment;  this  is  convenient  but  not  altogether 
necessary  if  method  of  procedure  is  followed  as  outlined.  Several  sets  of 
observations  should  be  taken  by  each  party,  each  set  giving  a  different  solar 
triangle  to  solve.  Preliminary  practice  in  pointing  the  telescope  at  the 
sun  will  be  necessary;  reduce  the  shadow  of  the  telescope  (thrown  on  a 
piece  of  paper)  to  a  small  circle,  when  the  sun  may  be  observed  through 
the  telescope,  or  its  image  seen  as  explained  in  the  "practical  suggestions," 
p.  625.  The  sun  may  be  also  approximately  found  by  turning  back  the 
colored  glass  of  the  prismatic  eyepiece  (in  transits  so  furnished)  and  revolv- 
ing the  telescope  about  each  axis  until  a  decided  glare  is  refracted  to  the 
eye,  which  must  be  held  some  distance  away.  Be  careful  not  to  use  either 
stadia  hair  by  mistake.  Be  certain  that  the  image  of  the  sun  seen  through 
the  prismatic  eyepiece  is  the  true  image;  a  false  image  much  smaller  is 
sometimes  visible  in  some  transits.  What  causes  it?  Check  the  transit 
work  as  to  horizontal  angles  at  the  close  of  each  set  of  observations  by 
turning  back  to  the  original  sight. 

Questions  concerning  the  sun  and  its  image:  1 .  What  is  the  sun's 
apparent  diameter  July  1?  Jan.  1?  What  causes  this  variation? 
p.  625.  2.  Does  this  apparent  diameter  vary  with  the  sun's  ' 
altitude?  3.  What  is  the  refraction  correction  for  bodies  on  the 
horizon?  bodies  at  an  altitude  of  45°?  bodies  at  the  zenith,  and 
why?  p.  624.  4.  Is  the  refraction  correction  additive  or  sub- 
tractive  as  applied  to  an  observed  altitude,  and  why?  p.  623. 


92  EXERCISES  nsr  DETERMINING  A  TRUE  MERIDIAN. 

5.  What  determines  the  amount  of  this  correction  other  than  a 
body's  altitude?  p.  623.  6.  Which  appears  to  us  larger,  the  sun 
or  the  moon? 

Questions  concerning  field  work:  7.  What  is  the  best  time  of 
day  for  observations  by  this  method?  p.  625.  8.  Why  invert  the 
telescope  before  taking  second  observation?  p.  625.  9.  Why  take 
the  two  observations  within  a  few  minutes?  p.  625.  10.  What  are 
errors  of  eccentricity  and  how  corrected?  11.  How  nearly 
should  azimuths  by  this  method  be  relied  on?  12.  What  is  the 
comparative  accuracy  of  two  observations  made  with  equal 
care,  one  at  8  A.M.  and  one  at  11?  13.  How  does  the  probable 
error  of  an  azimuth  obtained  by  a  single  observation  on  the  sun 
compare  with  that  of  one  from  Polaris  at  elongation?  14.  Give 
the  method  of  procedure  used  when  the  transit  has  a  prismatic 
eyepiece;  when  it  has  not. 

Questions  Concerning  the  Solution  of  the  Astronomical  Triangle 
for  Azimuth:  15.  Define  declination,  p.  621.  16.  Draw  the 
astronomical  triangle  for  the  sun  in  July  (declination  20°  north) , 
for  an  observation  about  9  A.M.  in  Latitude  40°  north.  17. 
Draw  it  for  the  sun  in  December  (declination  20°  south),  for 
an  observation  about  3  P.M.  in  Latitude  25°  north.  18.  When  is 
the  declination  of  the  sun  zero?  19.  When  does  it  change  most 
rapidly  and  how  much  is  the  change  per  hour?  When  most 
slowly  and  how  much  per  hour?  p.  622.  20.  Neglecting  refrac- 
tion, how  high  is  the  sun  in  the  sky  at  noon  on  March  22  in  Latitude 
40°  north?  21.  Is  the  time  used  in  the  solution  of  the  triangle? 
What  is  the  object  of  recording  it?  What  would  be  the  effect 
on  the  solution  of  an  error  of  five  minutes  in  the  recorder's  watch? 
22.  Explain  how  the  term  azimuth  is  understood  by  astronomers; 
by  surveyors.  23.  Compare  this  difference  with  the  difference 
between  the  beginning  of  the  astronomical  day  and  of  the  civil 
day.  24.  Is  it  necessary  to  know  the  longitude  with  accuracy? 
the  latitude?  25.  If  you  knew  neither  longitude,  latitude  nor 
time  precisely,  could  you  use  this  method  and  secure  accurate 
results? 


EXERCISES  IN  DETERMINING  A  TRUE  MERIDIAN.    93 

Exercise  M-3. 
Determination  of  a  Meridian  with  Solar  Attachment. 

References:  Appendix,  pp.  627-632. 

Equipment:  Transit  with  solar  attachment,  stakes,  ax. 

Note:  The  solar  attachment  may  be  either  Burt  (604  a)  or 
Saegmuller.  (604  b) .  In  case  the  transit  is  provided  with  another 
form  it  may  be  necessary  to  consult  the  maker's  catalogue  for 
some  suggestions  as  to  its  use.  The  principle  of  the  graphic 
solution  of  the  spherical  triangle  (see  Fig.  600)  is  common  to  all. 

Directions:  Determine  the  bearing  of  the  line  in  question  by 
setting  up  at  some  convenient  point  thereon  and  following  the 
method  of  procedure  outlined  on  pp.  630-632. 

Field  Notes:  These  should  include  latitude  of  place,  apparent 
declination  of  sun,  standard  time  of  observation  and  true  bearing 
obtained. 

Suggestions:  Read  carefully  Arts.  600-602,  and  604,  including  the  sug- 
gestions on  p.  631.  Many  of  the  suggestions  in  Exercise  M-2  apply  to  this 
exercise  as  well.  Be  sure  to  level  up  by  the  method  of  suggestion  (15), 
p.  89.  The  best  time  of  day  for  determination  of  a  meridian  by  this 
method  is  from  8.30  to  9.30  A.M.  or  2.30  to  3.30  P.M.,  as  the  sun's  appar- 
ent altitude  when  small  is  correspondingly  uncertain,  while  for  two  hours 
before  or  after  noon  its  path  is  so  slightly  inclined  to  the  horizon  as  to 
make  an  accurate  determination  by  this  method  difficult.  The  transit 
should  be  in  perfect  adjustment  throughout,  including  the  solar  attachment. 
For  adjustments  of  the  various  forms  of  solar  attachments  see  the  manufac- 
turers' catalogues.  Great  care  must  be  used  throughout,  in  the  use  of  this 
method,  not  to  disturb  or  jar  any  part  of  the  instrument  after  it  has  been 
set  in  position.  A  seemingly  insignificant  disturbance  may  render  the 
result  so  inaccurate  as  to  be  useless.  It  is  difficult  to  adjust  the  colored 
glass  without  deranging  some  part  of  the  instrument,  —  avoid  the  necessity 
for  this  where  possible.  It  is  advisable  not  to  depend  on  a  single  determi- 
nation of  bearing  by  this  method,  —  if  possible  take  a  number  at  various 
times  during  the  day.  Note  that  the  declination  change  from  8  A.M.  to 
4  P.M.  on  a  single  day  is  about  8  minutes  of  arc  in  March  and  September, 
but  is  nearly  zero  at  the  solstices.  Various  handbooks  issued  by  instru- 
ment makers  give,  with  sufficient  accuracy  for  the  purpose,  the  sun's 
declination  daily  throughout  the  year,  together  with  the  refraction  correc- 
tions for  various  latitudes.  For  a  representation  of  the  solar  spherical 
triangle  which  the  solar  attachment  solves  graphically,  see  Fig.  600. 

Questions:  1.  Does  the  refraction  correction  vary  with  the 
declination  only?  2.  When  is  it  greatest  and  when  least  in  Lati- 
tude 40°  north?  3.  On  what  does  it  directly  depend?  4.  Is  it 
additive  in  north  or  south  declination?  p.  631.  Why?  5.  Must 
a  similar  correction  be  applied  to  the  latitude?  6.  Draw  the 


94    EXERCISES  IN  DETERMINING  A  TRUE  MERIDIAN. 

astronomical  triangle  for  Latitude  45°  north,  assuming  the  time 
to  be  3  P.M.  on  Nov.  5  (declination  15^°  south).  7.  What  is  the 
sun's  apparent  path  for  a  single  day,  exactly?  approximately? 
p.  628.  8.  Define  declination,  azimuth,  hour  circle.  Art.  600. 
9.  How  does  the  local  time  enter  into  the  problem?  latitude? 
longitude?  10.  Which  must  be  known  most  accurately,  and 
how  large  an  error  is  permissible  in  each?  11.  What  will  be  the 
angle  between  the  vertical  planes  of  the  two  telescopes  (Saegmul- 
ler)  or  of  the  solar  attachment  and  the  telescope  (Burt)  at  the  close 
of  the  operation?  12.  How  may  it  be  measured  in  each  case  and 
what  does  it  represent?  13.  Article  604  (b)  (2)  mentions  an 
index  error  in  the  vertical  circle.  How  would  this  error  affect 
the  setting  off  of  the  declination?  14.  Is  the  solar  attachment 
applicable  for  use  with  a  star?  15.  What  are  the  principal 
differences  between  the  Burt  and  the  Saegmuller  solar  attach- 
ments? p.  631.  16.  Which  would  you  prefer  on  a  partly  cloudy 
day?  17.  Which  is  most  accurate?  18.  What  are  the  advan- 
tages and  disadvantages  of  the  solar  attachment  method  as 
compared  with  that  of  single  solar  altitudes?  Compare  their 
accuracy.  19.  What  should  be  the  limit  of  error  of  the  solar? 
How  does  either  solar  method  compare  with  the  Polaris  method? 

20.  Plot  the  curve  of  declination  of  the  sun  for  all  or  half  the  year. 

21.  What  is  the  cause  of  the  change?     22.  Does  it  go  through  a 
complete  cycle  in  a  year  of  365  days?     23.  What  other  forms  of 
solar  attachments  are  in  use  beside  the  Burt  and  Saegmuller, 
and  what  are  their  distinctive  features? 

Note:  If  desired  an  -exercise  may  be  given  in  determining  latitude  by  any 
one  of  the  three  methods  explained  on  pages  632-633. 


GROUP   I. 

A  STUDY  OF  SURVEYING  INSTRUMENTS. 

The  exercises  in  this  group  are  intended  for  class-room  discussions  of 
the  primary  parts  of  surveying  instruments  and  of  each  instrument  as  a 
whole.  For  the  reasons  given  on  page  537  it  is  well  to  postpone  most  of  these 
discussions  until  after  the  student  has  become  somewhat  accustomed  to  the 
use  of  instruments.  The  discussion  of  any  instrument  will  of  course  be  of 
much  greater  value  if  one  or  more  types  of  that  instrument  can  be  examined 
by  the  students  during  the  discussion.  Often  it  will  be  found  desirable 
to  take  an  instrument  apart  in  order  to  show  portions  which  are  otherwise 
invisible. 

Exercise  1-1. 
The  Vernier,  the  Magnetic  Needle  and  the  Level  Bubble. 

References:  Pages  538-545,  §§  565,  566  and  567. 

Questions:  1.  Who  invented  the  vernier?  p.  538.  2.  Of  what 
does  a  vernier  consist?  3.  What  is  meant  by  the  "  least  count  "? 
Illustrate  by  a  sketch,  or  by  constructing  a  rough  vernier  and 
scale  of  paper  or  cardboard.  4.  What  mark  on  a  vernier  usually 
serves  as  an  indicator?  p.  539.  5.  What  two  steps  are  involved 
in  any  reading  made  by  the  aid  of  a  vernier?  6.  What  is  the  sole 
use  made  of  the  vernier?  Remark,  p.  539.  7.  Illustrate  the 
method  of  reading  a  vernier  either  by  a  sketch  or  by  means  of  a 
rough  vernier  such  as  that  referred  to  in  the  second  question. 
8.  What  is  the  difference  between  a  direct  and  a  retrograde 
vernier?  p.  540.  Which  form  is  the  most  common?  When  are 
retrograde  verniers  used  and  how  are  they  read?  9.  Give  a 
general  rule  for  determining  the  least  count  of  a  vernier;  give  a 
simpler  rule.  10.  By  means  of  the  figures  on  page  230  explain 
how  to  read  a  vernier  on  a  leveling  rod  target,  and  point  out  the 
"  danger  points  "  where  mistakes  are  likely  to  occur.  11.  By 
means  of  the  figures  on  pages  78  to  82  explain  how  to  read 
verniers  on  transits  and  point  out  the  "  danger  points."  12. 
Describe  special  forms  of  verniers  such  as  a  "  folded  "  vernier,  p.  83. 

Questions  on  the  Magnetic  Needle:  See  Questions  under  Exercise 
Co-2,  page  70  of  this  book. 

Questions  on  the  Level  Bubble:  See  Questions  under  Exercise  L-l 
and  L-5,  pages  51  and  54  of  this  book. 

95 


96        A   STUDY   OF   SURVEYING   INSTRUMENTS. 

Exercise  1-2. 
Theory  of  Lenses. 

Reference:  Page  545,  §  568. 

Questions:  1.  What  three  forms  of  lenses  are  used  most  in 
telescopes?  p.  545.  Are  they  used  singly  or  in  combination? 
p.  546.  2.  Of  what  shape  is  each  surface  of  a  double  convex 
lens?  3.  Define  optical  center;  principal  focus;  principal  axis 
and  focal  length,  and  illustrate  by  means  of  a  sketch.  4.  Upon 
what  does  the  focal  length  depend?  If  the  focal  length  does  not 
depend  upon  the  size  of  the  lens,  why  is  it  usually  greater  for  a 
large  lens  than  for  a  small  one?  5.  Give  the  general  proposition 
concerning  a  cone  of  rays  emanating  from  a  principal  focus,  and 
illustrate  by  a  sketch.  6.  How  does  this  proposition  apply 
to  rays  from  the  sun?  p.  547.  7.  Give  the  general  proposition 
concerning  a  cone  of  rays  emanating  from  any  point  beyond  the 
principal  focus.  8.  Define  conjugate  foci;  secondary  axis.  9. 
From  a  principle  of  optics  state  the  relation  between  the  two 
distances  from  a  lens  to  conjugate  foci  and  the  focal  length  of  that 
lens.  10.  Give  the  general  proposition  concerning  a  cone  of 
rays  emanating  from  any  point  at  a  distance  from  the  lens  less 
than  the  focal  length,  p.  548.  11.  Define  virtual  conjugate  focus. 
12.  How  are  images  formed  by  a  lens?  13.  When  is  an  image 
real  and  inverted  and  when  virtual  and  erect?  14.  What  is  the 
fundamental  principle  of  the  magnifying  glass?  15  When  is 
no  image  formed?  16.  What  is  the  fundamental  principle  upon 
which  the  object  glass  of  a  telescope  is  constructed?  17.  How  far 
from  the  lens  of  a  camera  should  an  object  be  placed  to  be  photo- 
graphed exact  size?  (Prove  by  equation  (l),p.  547.)  How  far 
from  the  lens  must  the  object  be  if  the  photograph  is  smaller 
than  the  object?  Larger  than  the  object?  18.  To  what  is 
spherical  aberration  due?  p.  549.  To  what  is  chromatic  aberra- 
tion due?  19.  How  can  spherical  aberration  be  corrected?  How 
can  chromatic  aberration  be  corrected?  20.  What  is  an  achro- 
matic lens? 


A   STUDY    OF    SURVEYING   INSTRUMENTS.         97 

Exercise  1-3. 

The  Telescope. 

Reference:  Page  549,  §  569. 

Questions:  1.  What  is  the  function  of  the  object  glass  of  a 
telescope?  p.  549.  Of  the  eyepiece?  2.  What  is  the  difference 
between  an  inverting  and  a  non-inverting  telescope?  Where 
does  this  difference  lie?  3.  Explain  the  construction  of  an 
eyepiece.  How  may  it  be  centered?  4.  Explain  the  construc- 
tion of  the  objective.  How  is  it  moved  in  or  out  for  focusing? 
5.  Explain  the  construction  of  the  cross-hair  ring,  and  method 
of  attaching  cross-hairs.  6.  How  may  the  reticle  be  drawn  to 
one  side  or  the  other  of  the  telescope  tube?  Why  are  the  holes 
for  the  capstan  screws  left  unthreaded?  Why  is  it  necessary  to 
loosen  one  capstan  screw  before  tightening  the  opposite  screw? 
How  may  the  whole  ring  be  turned  slightly?  When  is  it  neces- 
sary to  turn  it?  7.  By  means  of  a  sketch,  illustrate  the  theory 
of  lenses  applied  to  a  non-erecting  telescope,  making  clear  what 
general  proposition  applies  to  the  objective  and  what  to  the  eye- 
piece, p.  550,  §  569  (b).  Explain  the  reason  for  the  rule  for 
focusing.  8.  By  means  of  a  sketch,  explain  the  difference 
between  an  erecting  and  a  non-erecting  eyepiece.  9.  Compare 
these  two  types  of  eyepieces,  giving  the  advantages  and  dis- 
advantages of  each.  Remark,  p.  553.  10.  Name  two  special 
forms  of  telescopes.  Note,  p.  553.  11.  What  can  you  say  regard- 
ing the  terms  "  line  of  collimation  "  and  "  line  of  sight  "?  12. 
Explain  three  defects  which  are  inherent  but  should  be  corrected 
in  telescopes.  13.  Upon  what  does  good  "  definition  "  depend? 
14.  What  is  "  illumination  "  and  upon  what  does  it  depend? 
What  is  the  relation  between  illumination  and  magnifying 
power?  15.  How  does  the  "  size  of  field  "  vary?  16.  Upon 
what  does  "  magnification "  depend?  Explain  the  relation 
between  magnifying  power  and  the  size  of  the  aperture;  the 
relation  between  magnifying  power  and  the  level-bubble  or  the 
vernier.  17.  Compare  high  power  and  low  power  telescopes, 
giving  the  advantages  a,nd  disadvantages  of  each.  p.  555.  18. 
For  a  given  length  of  telescope  why  can  the  power  be  increased 
by  using  a  non-erecting  instead  of  an  erecting  eyepiece?  19. 
For  a  given  power  how  is  the  height  of  standards  affected  by  the 
use  of  a  non-inverting  eyepiece,  and  why  is  this  an  advantage? 
20.  How  can  a  high  and  low  power  be  obtained  in  the  same 


98         A    STUDY    OF    SURVEYING    INSTRUMENTS. 

telescope,  and  what  are  the  advantages  of  such  a  telescope? 
Remark,  p.  555.  21.  What  is  "  parallax,"  and  how  may  it  be 
eliminated?  22.  Describe  the  tests  for  flatness  of  field,  p.  556; 
for  definition;  for  size  of  field;  for  size  of  aperture;  for  magnifying 
power.  (These  tests  should  be  made  by  each  student  if  circum- 
stances permit.)  23.  Summarize  the  principal  points  to  be 
remembered  in  connection  with  the  telescope  as  regards  the 
objective,  the  eyepiece,  the  magnifying  power,  parallax,  size  of 
aperture,  flatness  of  field  and  inherent  defects. 


Exercise  1-4. 
Chains  and  Tapes. 

Reference:  Page  559,  §  570. 

Questions:  See  page  6  of  this  book,  questions  12,  14,  15  and  16, 
and  page  9,  questions  1,  4,  5  and  6.  1.  Describe  how  a  standard 
may  be  established  for  use  in  ordinary  surveying,  p.  562.  2. 
Describe  a  method  for  testing  the  length  of  a  tape.  p.  562. 

Exercise  1-5. 
The  Transit. 

Reference:  Page  563,  §  571. 

Questions:  1.  What  are  the  three  principal  parts  of  a  transit? 
p.  563.  2.  Explain  how  either  the  upper  or  lower  plate  can  be 
revolved  without  turning  the  other,  or  how  both  can  be  revolved 
together.  3.  Explain  the  construction  of  the  inner  and  outer 
spindles.  4.  Explain  the  workings  of  the  different  parts  of  a 
transit  when  a  horizontal  angle  is  measured.  5.  What  are  the 
common  methods  of  numbering  the  graduations  on  the  limb? 
p.  67.  6.  Explain  how  the  various  set-screws  and  tangent- 
screws  work.  p.  564.  7.  If  a  transit  is  in  perfect  adjustment  and 
is  properly  set  up,  why  is  it  impossible  to  measure  with  it  any 
angle  which  is  not  a  horizontal  or  a  vertical  angle?  Remark,  p.  566. 
8.  What  are  some  of  the  special  attachments  for  the  transit  and 
their  uses?  9.  Name  some  of  the  most  important  requirements 
for  transits  as  regards  the  spindles,  p.  567;  the  limb  graduations; 
opposite  verniers;  provision  for  reading  vernier  accurately; 
relation  between  magnifying  power  of  telescope  and  least  count 


A    STUDY    OP    SURVEYING    INSTRUMENTS.          99 

of  vernier;  between  magnifying  power  and  sensitiveness  of  level- 
bubble;  clamps  and  screws;  tripod.  10.  Name  five  additional 
requirements  which  may  be  met  by  adjustments,  p.  568.  11. 
Give  the  test  for  eccentricity. 

Exercise  1-6. 
The  Level. 

Reference:  Page  569,  §  572. 

Questions:  1.  What  are  the  most  essential  qualities  in  tele- 
scopes for  levels?  p.  569.  2.  What  is  the  lower  limit  for  magnify- 
ing power?  3.  Why  can  the  magnifying  power  of  a  telescope 
for  a  level  be  greater  than  that  for  a  transit  telescope  and  still  be 
consistent  with  the  sensitiveness  of  the  level  bubble?  4.  Why  is 
the  upper  limit  for  magnifying  power  placed  at  from  36  to  40 
diameters  on  ordinary  levels?  5.  What  are  the  ordinary  limits 
for  sensitiveness?  6.  Upon  what  does  stability  depend?  7.  What 
are  the  two  distinguishing  characteristics  of  a  wye-level?  What  is 
the  object  of  this  construction?  8.  Explain  the  construction 
of  a  dumpy  level.  What  are  its  advantages  and  disadvantages? 
9.  Name  some  special  forms  of  levels.  10.  Describe  some  forms 
of  home-made  levels.  Note,  p.  571.  11.  Describe  some  of  the 
tests  for  the  level  not  made  in  the  ordinary  adjustments. 


Exercise  1-7. 
Leveling-rods  and  Stadia  Rods. 

References:  Pages  571  to  575,  §§  573  and  574. 

Questions  on  Leveling-Rods:  1.  What  is  the  difference  between 
a  target  rod  and  a  self-reading  or  speaking  rod?  p.  571.  2.  Which 
is  the  better  for  ordinary  leveling?  3.  What  is  the  difference 
between  a  New  York  rod  and  a  Philadelphia  rod?  4.  What 
two  common  types  of  target  are  most  used?  p.  572.  5.  What 
is  the  difference  between  a  target  with  a  scale  and  one  with  a 
vernier?  pp.  228-230.  6.  What  is  an  angle  target?  How  does 
it  help  in  "  plumbing  "  the  rod?  7.  Describe  some  special  forms 
of  leveling-rods.  8.  Describe  an  automatic  leveling-rod.  9. 
Describe  a  plumbing-level,  p.  573.  10.  What  two  tests  should  a 
good  leveling-rod  meet?  p.  232. 


100         A    STUDY   OF   SURVEYING   INSTRUMENTS. 

Questions  on  Stadia  Rods:  11.  Describe  the  target  stadia  rod. 
p.  573.  Is  it  often  used  in  practice?  12.  Give  some  of  the 
requirements  which  should  be  met  by  a  good  stadia  rod.  Com- 
pare the  forms  shown  on  page  574,  giving  the  advantages  and  dis- 
advantages of  each.  13.  Give  some  suggestions  for  making 
stadia  rods.  p.  574. 

Exercise  1-8. 
The  Compass,  the  Plane  Table  and  the  Sextant. 

References:  Page  575,  §  575. 

Questions  on  the  Compass:  See  page  70  of  this  book,  Questions 
13  to  21. 

Questions  on  the  Plane  Table:  See  page  79  of  this  book,  Questions 
1  to  4. 

Questions  on  the  Sextant:  1.  What  is  the  distinguishing  charac- 
teristic of  the  sextant?  p.  577.  2.  What  advantage  has  it  over 
other  instruments  used  for  measuring  angles?  p.  578.  3.  In 
what  kinds  of  work  is  the  sextant  most  used?  4.  Explain  the 
method  of  using  the  sextant  in  measuring  horizontal  angles. 
5.  Give  some  practical  suggestions  for  the  use  of  the  sextant, 
p.  579.  6.  How  are  vertical  angles  measured?  7.  By  means 
of  a  diagram,  explain  the  theory  of  the  sextant,  p.  579. 

Note:  In  connection  with  this  exercise  practice  should  be  given  in  measur- 
ing both  horizontal  and  vertical  angles  with  the  sextant.  Problems  similar 
to  that  on  page  137,  §  197,  may  be  assigned  by  the  instructor. 

Exercise  1-9. 
The  Care  of  Instruments. 

Reference:  Chapter  XLVII,  p.  607. 

Questions:  1.  What  are  some  of  the  things  to  avoid  in  using 
instruments?  p.  607.  2.  What  are  some  of  the  precautions  which 
should  be  taken?  p.  608.  3.  Give  suggestions  for  the  care  of 
steel  tapes,  p.  609.  4.  Give  suggestions  for  riveting  a  tape. 
5.  Give  suggestions  for  soldering  a  broken  tape.  p.  610.  6.  Give 
suggestions  for  emergency  repairs  to  a  tape  by  a  splice,  p.  611; 
by  rough  riveting.  7.  What  kind  of  lubricants  are  used  for 
instruments?  Which  is  the  best?  8.  How  may  screws  and 


A    STUDY    OF    SURVEYING   INSTRUMENTS.          101 

screw-holes  be  cleaned?  p.  612.  9.  How  may  graduated  arcs  be 
cleaned?  10.  How  may  bubble  tubes  be  replaced?  p.  613.  11. 
Give  suggestions  for  the  care  of  lenses,  p.  614;  of  focusing  slides. 
12.  Explain  in  detail  the  method  of  replacing  broken  cross-hairs. 
p.  616.  13.  How  may  dust  be  removed  from  cross-hairs?  •  14. 
Give  suggestions  for  the  care  of  tripods.  15.  Give  suggestions 
for  the  care  of  centers,  spindles  and  centers. 

Note:  It  is  well  to  give  the  student  an  opportunity  to  make  some  of  the 
repairs  suggested  by  the  above  questions.  Especially  should  he  have  an 
opportunity  to  replace  cross-hairs  and  to  mend  a  broken  tape. 


GROUP  A. 

ADJUSTMENTS. 

The  exercises  in  this  group  afford  practice  in  the  adjustments  of  all  of  the 
surveying  instruments  in  common  use.  As  pointed  out  in  the  introductory 
note  to  Chapter  XL VI,  page  581,  the  student  should  understand  clearly  the 
reason  for  each  step  of  an  adjustment,  otherwise  the  exercises  will  be  of 
little  value. 

GENERAL  DIRECTIONS  FOR  EXERCISES  A-l  TO  A-7. 

Each  student  should  work  at  each  adjustment  until  it  is  satis- 
factorily completed.  It  is  suggested  that  in  large  classes  men 
working  on  the  same  adjustment  should  be  under  the  close  super- 
vision of  an  instructor,  and  that  a  general  discussion  of  each  ad- 
justment of  an  instrument  be  held  before  beginning  the  next 
adjustment  of  that  instrument.  When  there  are  a  number  of 
adjustments,  as  in  the  case  of  the  transit,  this  breaking  of  the  con- 
tinuity of  the  work  may  give  to  students  the  false  impression  that 
the  process  is  a  long  and  difficult  one.  For  this  reason  when  all 
of  the  adjustments  of  an  instrument  have  been  completed  by  the 
students,  it  is  well  for  the  instructor  to  adjust  the  same  instru- 
ment as  rapidly  as  possible  in  the  presence  of  the  entire  squad, 
emphasizing  the  logical  order  of  the  adjustments  and  showing 
how  one  may  affect  another. 

It  is  presupposed  that  the  discussions  in  Group  I,  pages  95-101, 
have  been  held  before  beginning  adjustments,  and  that  a  thorough 
study  of  the  different  parts  of  instruments  has  been  made.  Of 
special  importance  are  the  questions  on  the  construction  of  the 
telescope  and  the  control  of  the  cross-hair  ring  in  Exercise  1-3, 
p.  97  of  this  book;  also  questions  on  the  construction  of  the  transit 
and  of  the  level,  Exercises  1-5  and  7-6. 

Exercise  A-l. 
Preliminary  Discussion  of  Adjustments. 

References:  Pages  581  to  583. 

Questions:  1.  Why  are  certain  of  the  parts  of  an  instrument 
made  adjustable?  p.  581.  2.  Can  accurate  work  be  done  with  an 
instrument  out  of  adjustment?  Can  all  errors  be  eliminated 
without  adjusting  the  instrument?  3.  How  long  may  a  good 

102 


ADJUSTMENTS    OF    INSTRUMENTS.  103 

instrument  stay  in  adjustment?     How  often  should  it  be  tested? 

4.  What  are  the  two  steps  in  each  adjustment  of  any  instrument? 

5.  What  precaution  should  be  taken  to  avoid  wear  on  holes  in 
capstan  screws  and  nuts?  p.  582.     6.  Should  each  adjustment  be 
perfected  before  beginning  the  next?     What  should  be  the  final 
step?     7.  In    making   any   one    adjustment    how   many   times 
should  the  test  and  correction  be  repeated?     How  may  time  be 
saved?     8.  What  precautions  may  be  taken  to  cause  an  instru- 
ment   to   "  hold  "  its    adjustments?      9.  Give    suggestions    for 
working  the   capstan  screws  of    a   cross-hair  ring.     10.  Which 
cross-hair  should  be  adjusted  first.     11.  Define  line  of  sight;  line 
of  collimation.     12.  If  after  adjustment  the  intersection  of  the 
cross-hairs  appears  to  be  out  of  the  center  of  the  field  of  vision 
what  is  generally  the  trouble?     13.  How  is  parallax  eliminated? 
p.  555.     14.  Why  is  it  well  to  set  up  an  instrument  in  the  shade 
during  adjustments?    15.  By  means  of  a  sketch,  explain  with  care 
the  method  of  reversion.     16.  Show  how  this  principle  is  involved 
in  the  adjustment  of  a  home-made  A-level  explained  in  the  note 
on  page  571. 

Note:  Since  the  method  of  reversion  is  the  basis  of  every  adjustment,  it 
should  be  discussed  carefully  and  understood  thoroughly  before  any  attempt 
is  made  to  adjust  an  instrument. 

Exercise  A-2. 
Adjustments  of  the  Transit. 

Reference:  Pages  581-591. 

Equipment :  Transit,  steel  tape,  leveling-rod,  sight  pole,  adjust- 
ing-pins, ax  and  stakes. 

Directions:  1.  Set  up  the  transit,  selecting  if  possible  a  level 
place  where  300-ft.  sights  backward  and  forward  in  a  straight  line 
may  be  taken,  and  where  the  telescope  can  be  directed  to  some 
well-defined  high  point.  2.  Perform,  in  turn,  each  of  the  five 
principal  adjustments  of  the  transit  by  the  methods  explained  on 
pages  581-591,  paying  particular  attention  to  the  reason  for  each 
step.  (See  also  General  Directions  on  page  102  of  this  book.) 

General  Questions  on  the  Adjustment  of  a  Transit:  1.  What  are 
the  five  principal  lines  of  a  transit?  p.  584.  (Illustrate  with  a 
transit.)  2.  Is  it  as  important  that  the  plate  levels  should  be  in 
perfect  adjustment  when  using  the  transit  in  level  country  as 
when  using  it  in  hilly  country?  3.  When  is  it  important  that  the 


104  ADJUSTMENTS    OF    INSTRUMENTS. 

line  of  sight  should  move  in  a  vertical  plane  (second  and  third 
adjustments)?  4.  What  kind  of  work  requires  that  the  tele- 
scope level  should  be  in  adjustment?  5.  Why  is  it  not  essential 
in  measuring  vertical  angles  that  the  vertical  circle  should  be  in 
adjustment?  Caution,  p.  98. 

Questions  on  the  Adjustment  of  the  Plate  Levels:  (To  be  discussed 
before  the  second  adjustment  is  begun.)  6.  What  is  the  object 
of  this  adjustment?  p.  584.  7.  Describe  the  test.  p.  585.  8. 
Explain  the  method  of  correction  and  state  the  principle  involved. 
9.  When  the  final  test  is  satisfactory  how  can  non-parallelism  in 
the  axes  of  the  inner  and  outer  spindle  be  detected?  Suggestions, 
p.  585.  10.  Why  is  it  best  to  adjust  the  plate  levels  with  the 
lower  plate  clamped  and  the  upper  plate  undamped?  11.  How 
can  you  tell  in  which  direction  to  turn  a  capstan  screw?  p.  586. 

Questions  on  the  Adjustment  of  the  Cross-hairs:  (To  be  discussed 
before  the  third  adjustment  is  begun.)  12.  Why  is  the  hori- 
zontal hair  adjusted  first?  p.  582?  (7).  13.  What  preliminary 
step  may  be  taken?  Note,  p.  586.  14.  What  kind  of  work  is 
affected  by  the  adjustment  of  the  horizontal  hair?  15.  What  is 
the  object  in  the  adjustment  of  the  horizontal  hair?  16.  The 
test?  17.  Method  of  correction?  18.  Is  it  necessary  that  the 
telescope  should  be  horizontal  during  the  adjustment  of  the  hori- 
zontal hair?  19.  Why  should  one  point  sighted  at  be  near  the 
transit,  the  other  far  away?  20.  Give  practical  suggestions 
for  the  adjustment  of  the  horizontal  hair.  p.  587.  21.  When 
the  horizontal  hair  is  moved  up  or  down  is  the  vertical  hair 
moved?  Note,  p.  550.  22.  Suppose  that  in  a  telescope  in 
which  the  eyepiece  is  erecting  the  horizontal  hair  should  appar- 
ently be  moved  downward,  which  capstan  screw  is  loosened 
and  which  tightened?  p.  11.  23.  What  kind  of  work  is  affected 
by  the  adjustment  of  the  vertical  hair?  p.  586.  24.  What  is 
the  object  in  the  adjustment  of  the  vertical  hair?  p.  587.  25.  The 
test?  26.  The  method  of  correction?  27.  Why  measure  only 
one  quarter  of  the  distance  between  the  two  points?  (Explain 
by  diagram.)  28.  Suppose  the  vertical  hair  is  apparently  to 
the  right  of  the  third  point,  which  screw  should  be  loosened  and 
which  tightened  if  the  eyepiece  is  erecting?  p.  589,  (6).  29.  Give 
some  practical  suggestions  for  adjusting  the  vertical  cross-hair. 
30.  Suppose  that  after  the  cross-hairs  have  been  adjusted  the 
eyepiece  is  taken  out  or  disturbed  in  any  way,  would  this  affect 
the  adjustment  of  the  hairs?  p.  589. 


ADJUSTMENTS    OF   INSTRUMENTS.  105 

Questions  on  the  Adjustment  of  the  Standards:  31.  What  kind 
of  transit  work  is  affected  by  this  adjustment?  p.  584.  32.  What 
is  the  object  of  this  adjustment?  p.  589.  33.  The  test?  34. 
Method  of  correction?  35.  Principle  involved?  36.  If  the  second 
point  obtained  in  the  test  falls  to  the  right  of  the  first,  which  end 
of  the  supporting  axis  is  the  higher?  37.  Give  some  practical 
suggestions  for  adjusting  the  standards,  p.  591. 

Questions  on  the  Adjustment  of  the  Telescope  Level:  38.  What 
is  the  object  of  this  adjustment?  p.  591.  39.  When  is  it  neces- 
sary to  pay  particular  attention  to  this  adjustment?  p.  591. 
40.  What  other  instrument  is  always  adjusted  by  the  "peg 
method"?  p.  601,  I.  41.  Explain  by  means  of  a  diagram  the 
test  and  the  method  of  correction.  (See  also  questions  in  connec- 
tion with  "peg"  adjustment,  p.  107  of  this  book.) 

Questions  on  the  Adjustment  of  the  Vertical  Circle:  42.  What 
is  the  object  of  this  adjustment?  p.  591.  43.  The  test?  44. 
Method  of  correction? 

Questions  on  Centering  the  Eyepiece  and  the  Object-glass  Slide: 
45.  If  the  intersection  of  the  cross-hairs  is  obviously  out  of  the 
center  of  the  field  of  view  does  this  necessarily  indicate  that 
the  instrument  is  out  of  adjustment?  p.  601.  Does  it  affect  the 
accuracy  of  the  work?  46.  Explain  how  to  center  the  eyepiece. 
47.  How  do  the  screws  which  move  the  centering  ring  differ  in 
different  instruments?  p.  602.  48.  Why  does  not  the  center- 
ing of  the  eyepiece  affect  other  adjustments?  49.  Why  is  no 
provision  made  for  centering  a  non-erecting  eyepiece?  50.  What 
can  you  say  regarding  the  centering  of  the  object-glass  slide? 
Explain  the  method. 

Note:  It  is  well  to  give  the  student  an  opportunity  to  actually  center  an 
eyepiece,  either  in  connection  with  this  exercise  or  during  the  adjustment 
of  the  level. 

Exercise  A-3. 
Adjustments  of  the  Wye-Level. 

Reference:  Pages  592-600. 

Equipment:  Level,  one  or  preferably  two  leveling-rods,  steel 
tape,  adjusting-pins,  ax  and  stakes. 

Directions:  1.  Set  up  the  level  in  a  shady  place  where  a 
300-ft.  sight  may  be  taken  over  approximately  level  ground. 
2.  Perform  in  turn  each  of  the  three  principal  adjustments  of 


106  ADJUSTMENTS    OF    INSTRUMENTS. 

a  wye-level  by  the  methods  explained  on  pages  592  to  600. 
(See  also  General  Directions  on  page  102  of  this  book.)  3.  All 
three  adjustments  having  been  completed  apply  the  "peg 
method"  test. 

General  Questions  on  the  Adjustment  of  a  Wye-Level:  1.  What 
are  the  seven  principal  lines  of  a  wye-leyel?  p.  592.  (Illustrate 
with  a  level.)  2.  What  is  the  object  of  the  principal  adjust- 
ments? 3.  How  is  the  line  of  sight  made  to  coincide  with  the 
axis  of  the  collars?  4.  How  is  the  axis  of  the  bubble  made 
parallel  to  the  axis  of  the  level-bar?  p.  593. 

Questions  on  the  Adjustment  of  the  Cross-hairs:  (To  be  discussed 
before  the  second  adjustment  is  begun.)  5.  What  is  the  object 
of  this  adjustment?  6.  Describe  the  test.  7.  Explain  the 
method  of  correction  and  state  the  principle  involved.  8.  Is 
it  necessary  to  level  up  for  this  adjustment?  Suggestions,  p.  594. 
9.  Give  suggestions  for  working  the  capstan  screws.  10.  If 
there  are  two  sets  of  capstan  screws  which  set  is  used?  1 1 .  How 
may  the  horizontal  hair  be  tested  to  ascertain  if  it  is  truly  hori- 
zontal? If  it  is  not,  how  is  the  correction  made?  12.  What 
defects  in  construction  may  be  revealed  by  focusing  on  a  point 
near  the  instrument  and  repeating  the  test? 

Questions  on  the  Adjustment  of  the  Bubble  Tube:  (To  be  dis- 
cussed before  the  third  adjustment  is  begun.)  13.  What  is  the 
object  of  the  first  step?  p.  594.  14.  Describe  the  test.  15. 
Explain  the  method  of  correction  and  the  principle  involved. 
16.  Is  this  first  step  an  important  one?  Practical  suggestions, 
p.  595.  17.  If  the  tube  is  conical  how  will  the  bubble  move 
during  the  test?  Can  this  be  remedied?  18.  Why  put  on  the 
sunshade?  19.  What  is  the  object  of  the  second  step  in  the 
adjustment  of  the  bubble  tube?  p.  595.  20.  Describe  the  test. 

21.  Explain  the  method  of  correction  and  the  principle  involved. 

22.  What  precaution  should  be  taken  in  turning  the  telescope 
end  for  end?     Practical  suggestions,  p.  596.     23.    Give  sugges- 
tions for  working  capstan  nuts.     24.    Could  this  adjustment  be 
made  independent  of  the  wyes?     25.    Explain  under  what  condi- 
tions this  method  of  adjustment  fails. 

Questions  on  the  Adjustment  of  the  Wyes:  26.  What  is  the 
object  of  this  adjustment?  27.  Describe  the  test.  28.  Ex- 
plain the  method  of  correction  and  the  principle  involved.  29. 
Explain  why  undue  importance  is  often  attached  to  this  adjust- 


ADJUSTMENTS    OF   INSTRUMENTS.  107 

ment.  Practical  suggestions,  p.  597.  30.  Why  is  it  well  to 
make  alternate  tests  over  different  pairs  of  leveling  screws? 
31.  Give  suggestions  for  working  capstan  nuts.  32.  When 
unable  to  perfect  the  adjustment  where  should  one  look  for  the 
trouble?  33.  Why  should  the  "peg-method"  test  be  made? 
Remark,  p.  597.  When  may  this  test  be  omitted? 

Note:  For  questions  on  the  "peg  adjustment"  see  the  next  exercise. 
See  p.  105  of  this  book  for  questions  on  centering  the  eyepiece. 

Exercise  A-4. 
Adjustments  of  the  Dumpy  Level. 

References:  Pages  597  to  601. 

Equipment:  Dumpy  level,  two  leveling-rods,  steel  tape,  ad- 
justing-pins, ax  and  stakes. 

Directions:  1.  Set  up  the  level  in  a  shady  place  where  200-ft. 
sights  may  be  taken  in  opposite  directions  over  approximately 
level  ground.  2.  Perform  in  turn  each  of  the  two  adjustments, 
using  the  first  "peg  method"  for  the  first  adjustment.  3.  When 
the  adjustments  have  been  completed  apply  the  second  "peg 
method. "  (See  also  Practical  suggestions,  p.  599.) 

Questions  on  the  "Peg  Adjustment:"  (To  be  discussed  either 
just  before  or  just  after  the  first  adjustment  of  the  dumpy 
level.)  1.  What  is  the  object  of  this  adjustment?  p.  597. 
2.  By  means  of  a  figure,  explain  the  test  used  in  the  first  "peg 
method, "  and  derive  an  expression  for  the  error,  p.  598.  3. 
What  two  methods  of  correction  are  there?  Explain  the  first 
method;  the  second.  4.  If  the  line  of  sight  is  inclined  down- 
ward is  the  error  added  or  subtracted?  Practical  suggestions, 
p.  599.  5.  Give  suggestions  for  choosing  positions  of  pegs. 
6.  Why  should  more  than  one  pair  of  readings  be  taken  at  the 
first  set-up?  7.  After  the  final  adjustment  of  the  target  why 
should  the  rod  be  held  at  the  stake  nearer  the  level?  8.  What 
defects  of  a  wye-level  may  be  disclosed  by  the  "peg-method" 
test?  How  may  they  be  remedied?  9.  In  applying  the  peg 
adjustment  to  a  transit  or  a  wye-level  is  it  better  to  adjust  the 
cross-hairs  or  the  bubble  tube?  10.  By  means  of  a  figure, 
explain  the  test  for  the  second  "peg  method."  p.  600.  11. 
Explain  the  method  of  correction  and  the  principle  involved, 
12.  Explain  a  modified  method  of  the  peg  adjustment,  p.  600. 


108  ADJUSTMENTS   OF   INSTRUMENTS. 

Questions  on  the  Adjustments  of  the  Dumpy  Level.  13.  What 
are  the  principal  lines  of  the  dumpy  level?  p.  600.  14.  What 
is  the  object  of  the  first  adjustment?  p.  601.  15.  What  is  the 
test  and  correction?  16.  As  a  rule  is  it  better  to  adjust  the 
cross-hairs  or  the  bubble  tube?  Why?  17.  Why  do  some 
engineers  prefer  a  dumpy  level  with  a  non-adjustable  bubble 
tube?  18.  What  is  the  object  of  the  second  adjustment? 
19.  What  is  the  test  and  correction?  20.  Explain  how  to 
adjust  a  dumpy  level  on  which  no  provision  has  been  made  for 
raising  or  lowering  the  standards. 

Note:  See  p.  105  of  this  book  for  questions  on  centering  the  eyepiece. 

Exercise  A-5. 
Adjustments  of  the  Compass. 

Reference:  Pages  602-603. 

Equipment:  Compass,  adjusting-pins,  plumb-bob  and  string, 
fine  file,  pliers  or  small  brass  wrench. 

Directions:  Make  the  tests  for  each  of  the  four  adjustments 
of  the  compass.  For  obvious  reasons  it  will  usually  be  imprac- 
ticable in  class  work  to  make  the  corrections  in  the  last  three 
adjustments. 

Questions:  1.  What  is  the  object  in  the  adjustment  of  the 
levels?  p.  602.  Give  the  test  and  the  method  of  correction. 
2.  What  is  the  object  in  the  adjustment  of  the  sights?  Explain 
the  test  and  method  of  correction.  3.  What  is  the  object  in 
the  adjustment  of  the  needle?  p.  603.  Explain  the  test  and  the 
method  of  correction.  Give  some  practical  suggestions  for  this 
adjustment.  4.  What  is  the  object  in  the  adjustment  of  the 
pivot  point?  Explain  the  test  and  the  method  of  correction. 
5.  Explain  other  tests  for  the  compass,  p.  576.  6.  How  may 
the  needle  be  balanced?  p.  612;  how  may  it  be  remagnetized? 

Exercise  A-6. 
Adjustments  of  the  Plane  Table. 

Reference:  Pages  603-604. 

Equipment:  Plane  table  and  accessories,  adjusting-pins,  level- 
ing-rod,  steel  tape,  ax  and  stakes. 


ADJUSTMENTS   OF   INSTKUMENTS.  109 

Directions:  Make  in  turn  each  of  the  five  adjustments  of  the 
plane  table. 

Questions:  1.  Explain  the  adjustment  of  the  levels,  p.  604. 
2.  Explain  the  adjustment  of  the  board.  3.  Explain  the 
adjustment  of  the  telescope.  4.  How  may  the  line  of  sight 
and  the  edge  of  the  ruler  be  made  to  lie  either  in  the  same  ver- 
tical plane  or  in  parallel  planes?  Is  this  essential?  Remark, 
p.  604.  5.  Explain  the  adjustment  of  the  telescope  level.  6. 
Explain  the  adjustment  of  the  vertical  circle.  7.  Explain  other 
tests  for  the  plane  table,  p.  577. 


Exercise  A-7. 
Adjustments  of  the  Sextant. 

Reference:  Pages  604-606. 

Equipment:  Sextant,  two  blocks  of  wood  or  other  objects  of 
equal  height,  screw-driver. 

Directions:  Make  in  turn  each  of  the  four  adjustments  of  the 
sextant. 

Questions:  1.  Explain  the  adjustment  of  the  index-glass, 
p.  604.  2.  Explain  the  adjustment  of  the  horizon-glass,  p.  605. 
Give  some  practical  suggestions  for  this  adjustment.  3.  Ex- 
plain the  adjustment  of  the  telescope.  Give  suggestions.  4. 
Explain  the  method  of  determining  the  index-error,  p.  606.  Give 
suggestions. 


PART  II. 

EXERCISES   IN   OFFICE   WORK. 


Introductory. 

THE  first  seven  groups  of  exercises  in  Part  II  are  problems  in 
office  computation,  while  the  remaining  exercises  are  devoted  to 
plotting  and  mapping.  In  each  of  these  two  kinds  of  work 
exercises  are  arranged  in  a  progressive  order,  but  it  is  intended 
that  problems  should  be  given  alternately,  first  in  one  and  then 
in  the  other,  so  that  the  student  may  have  practice  both  in  com- 
puting and  in  plotting  from  the  beginning  of  the  course.  There 
is  a  decided  advantage  in  thus  carrying  on  the  two  kinds  of 
work  side  by  side. 

It  is  suggested  that  a  separate-leaf  notebook  about  8  x  10^ 
inches  be  used  for  all  computations.  Each  problem  should 
be  numbered  to  correspond  to  the  number  in  this  book,  and 
dated.  It  is  well  at  the  top  of  each  page  to  insert  a  heading 
which  will  show  at  a  glance  the  nature  of  the  problems  on  that 
page.  After  problems  have  been  checked  they  should  be  reinserted 
in  the  notebook,  carefully  arranged  in  order  for  future  reference. 
As  problems  in  one  exercise  frequently  involve  work  already 
done  in  a  previous  exercise,  this  arrangement  is  important. 

Throughout  the  course,  checking  computations  should  be  con- 
sidered just  as  much  a  part  of  the  work  as  making  the  compu- 
tations in  the  first  place.  (See  p.  362,  §  420.)  Much  valuable 
training  will  be  lost,  moreover,  if  the  student  does  not  constantly 
strive  to  acquire  the  systematic  methods  of  procedure  which 
help  so  much  in  avoiding  mistakes  as  well  as  in  saving  time. 
(Seep.  383,  §  421.) 

All  page  references  in  Part  II  marked  with  an  asterisk  (as  for 
example,  p.  112*)  refer  to  pages  in  this  book.  All  other  page 
references  are  to  pages  in  the  author's  text-book  on  Plane  Sur- 
veying. 

Since  instructors  may  desire  to  insert  additional  problems,  the 
numbering  of  problems  is  not  continuous,  intervals  being  left  at 
the  end  of  nearly  every  set. 

110 


GROUP  G. 

GENERAL  METHODS  OF  COMPUTATION. 

The  aim  in  this  group  of  exercises  is  to  afford  practice  in  the  general 
methods  of  computation  used  in  office  work. 

Exercise  G-l. 
Short  Cuts  in  Arithmetical  Work. 

References:   Pages  362  to  377. 

Problems:  1.  Explain  how  to  multiply  mentally  42  by  36, 
p.  364,  §  424  (a).  2.  Reduce  38  cubic  yards  to  cubic  feet 
mentally,  p.  364.  3.  Multiply  4821  by  819,  p.  364,  §  424  (b). 
4.  Divide  562981  by  72,  p.  365,  §  424  (c).  5.  Multiply  589432 
by  43416,  carrying  the  result  accurately  to  five  places,  p.  365, 
§  424  (d).  6.  Multiply  589432  by  43416,  using  the  usual  method 
of  long  multiplication,  and  check  the  result  by  casting  out 
nines,  p.  366,  §  424  (h).  7.  Divide  58.264362  by  5.2314,  carry- 
ing the  result  to  four  places  (i.e.,  two  decimal  places),  p.  366, 
§  424  (g).  8.  Divide  58.264362  by  5.2314  by  the  ordinary 
method  of  long  division  and  check  the  result  by  casting  out 
nines,  p.  367,  §  424  (i).  9.  Explain  how  to  square  mentally 
44,  55,  7i,  71,  p.  367,  §  424  (j).  10.  Find  mentally  the  square 
root  of  73  to  two  decimal  places,  p.  368,  §  424  (k).  11.  Ex- 
tract the  square  root  of  78620  by  the  approximate  method, 
p.  368,  §  424  (1).  12.  Explain  the  method  of  checking  by 
"Second  Differences,"  p.  368.  13.  Check  the  result  of  prob- 
lems 6  above  by  excess  of  ll's,  p.  369. 

Questions:  1.  Explain  by  illustrations  different  from  those 
given  in  the  book  at  least  four  general  methods  of  checking 
computations,  p.  362.  2.  Name  some  of  the  approximate 
checks  to  be  used  in  office  work,  p.  363.  3.  Give  some  sug- 
gestions for  saving  time  in  office  work,  p.  364.  4.  What  is  the 
main  object  in  grouping  like  operations  in  addition  to  saving 
time?  p.  364,  §  423. 


Ill 


112    GENERAL  METHODS  OF  COMPUTATION. 

Exercise  G  2. 
Consistent  Accuracy  in  Computations. 

Reference:  Page  369,  §  425. 

Note:  The  student  should  study  §  425  with  great  care  before  working 
the  problems.  The  importance  of  this  exercise  can  hardly  be  overesti- 
mated. There  is  probably  no  one  thing  in  office  work  so  costly  in  time 
and  money  as  the  carrying  of  computations  to  an  unnecessary  and  unwar- 
ranted number  of  figures.  The  student  will  be  well  repaid  for  all  the  study 
he  may  put  upon  this  subject. 

PROBLEMS. 

14.  A  lot  is  724.3  feet  by  64.6  feet.     Compute  its  area  to  as 
many  places  as  the  data  will  permit.     (See  illustration  I,  p.  373.) 

15.  Same  as  problem  14  except  the  lot  is  724.35  feet  by  64.62 
feet.     (See  illustration  II,  p.  373.) 

16.  The  radius  of  a  circle  is  2.167.     Find  the  length  of  its 
circumference  to  as  many  places  as  the  data  will  permit.     (See 
illustration  III,  p.  373.) 

17.  The  base  of  a  triangle  is  given  as  34.532  and  the  adjacent 
angle    as   27°    27'.      If    the    triangle    is    right-angled,  what    is 
the   length  of    the  perpendicular    side?     (See    illustration   IV, 
p.  373.) 

18.  Same  as  problem  17  except  the  angle  to  the  nearest  10" 
is  27°  27'.     (See  illustration  V,  p.  373.) 

19.  Same  as  problem  17  except  that  the  base  is  given  as  34.5 
feet.     (See  illustration  VI,  p.  373.) 

20.  The  length  of  a  line  is  given  by  the  lengths  of  four  seg- 
ments as  follows:  AB  =  354  feet,  BC  =  3521  feet,  CD  =  21.69 
feet,  DE  =  1.432  feet.     What  is  the  total   length  of  the  line 
AE  expressed  to  as  many  places  as  the  data  warrant? 

21.  The  circumference  of  a  circle  is  given  as  21.6  feet.     Ex- 
press its  radius  to  as  many  places  as  the  above  length  of  the 
circumference  will  permit. 

22.  The  perpendicular  side  of  a  right-angled  triangle  is  given 
as  4368  feet  and  the  base  as  4800  feet.     If  the  latter  measure- 
ment was  taken  to  the  nearest  100  feet,  express  the  tangent  of 
the  angle  to  as  many  places  as  the  data  will  permit. 


GENERAL  METHODS  OF  COMPUTATION.    113 

Questions:  I.  It  is  stated  that  25  men  surveyed  a  line  25 
miles  long.  What  is  the  essential  difference  between  the  num- 
ber 25  as  applied  to  men  and  as  applied  to  miles?  2.  How 
many  certain  figures  in  the  first  "25";  in  the  second  "25"? 
3.  Explain  why  consistent  accuracy  is  not  gained  by  carrying 
all  numbers  to  the  same  number  of  decimal  places,  p.  370, 
§  425  (a).  4.  What  must  one  know  in  order  to  determine  how 
many  certain  figures  there  are  in  numbers  ending  with  ciphers, 
as,  for  example,  the  number  4000?  p.  370,  §  425  (b).  5.  How 
many  certain  figures  are  contained  in  the  number  0.0051, 
p.  370?  6.  Illustrate  the  effect  of  uncertain  figures  in  addition 
and  multiplication,  p.  371.  7.  Give  the  general  method  of 
multiplication,  p.  372,  §  425  (g).  8.  Give  general  suggestions 
for  retaining  and  dropping  figures  in  computations,  p.  372. 


Exercise  G-3. 

Trigonometric  Relations  Between  the  Sides  of  a  Right- 
Angled  Triangle. 

Reference:  Page  640. 

Note:  The  trigonometric  relations  between  the  sides  of  a  right-angled 
triangle  are  most  easily  remembered  by  keeping  in  mind  the  fact  that  to 
obtain  a  side  of  a  triangle  a  trigonometric  function  is  always  multiplied 
by  the  radiits  of  a  circle.  The  purpose  of  this  exercise  is  to  review  the 
trigonometric  methods  of  solving  right  triangles. 

Directions:  1.  Draw  carefully  with  drawing  instruments  a 
right-angled  triangle  ABC,  whose  base  AB  is  8.62  inches  and 
whose  perpendicular  side  BC  is  6.24  inches  (use  the  side  of  the 
scale  divided  to  50ths  of  an  inch).  2.  Draw  the  arc  of  a  cir- 
cle, beginning  at  B  with  A  as  a  center  (radius  A  B}  correspond- 
ing to  the  first  quadrant  in  trigonometry.  3.  From  this 
figure  BC  is  evidently  tangent  to  the  circle,  and  the  radius  of 
the  circle  is  AB;  hence,  AB  multiplied  by  the  tangent  of  CAB 
will  give  the  length  of  BC ;  or,  what  is  the  same  thing,  BC  divided 
by  AB  (the  radius)  gives  the  tangent  of  CAB.  Likewise,  AB 
multiplied  by  the  secant  of  CAB  will  give  the  length  of  AC. 

Problem  23:  1.  Find  the  natural  tangent  of  CAB  in  the  above 
triangle  to  as  many  decimal  places  as  the  data  will  warrant. 
2.  Look  up  in  the  table  of  natural  tangents  the  corresponding 


114    GENERAL  METHODS  OF  COMPUTATION. 

value  of  CAB.  3.  Find  the  length  of  AC  by  multiplying  AB 
by  the  secant  of  CAB,  or,  what  is  the  same  thing,  by  dividing 
AB  by  the  cosine  of  CAB.  4.  Check  the  length  of  AC  by 
squaring  A B  and  BC,  using  the  table  of  squares,  p.  683;  also 
by  scaling  the  length  of  A C  on  the  drawing. 

Directions:  Draw  the  same  triangle  ABC,  but  with  A  as  a 
center  and  AC  as  a  radius  draw  an  arc  corresponding  to  the  first 
quadrant.  Functions  will  now  be  multiplied  by  AC  (the  radius) 
instead  of  A  B,  the  triangle  lying  wholly  within  the  quadrant. 

AC  sin.  CAB  =  BC 
AC  cos.  CAB  =  AB 

Problem  24:  Using  the  values  of  AC  and  of  CAB  found  in 
the  preceding  problem,  find  the  lengths  of  CB  and  AB  by  the 
above  formulas  to  as  many  places  as  the  data  will  warrant. 

Note:  The  student  will  observe  that  when  a  triangle  lies  wholly  within 
the  quadrant  (i.e.,  its  hypothenuse  is  the  radius  of  the  arc)  the  sine  and 
cosine  are  the  functions  used,  whereas,  if  it  extends  outside  of  the  quad- 
rant (i.e.,  the  base  is  the  radius)  the  tangent,  cotangent,  secant  and  cosecant 
are  used.  When,  as  in  many  books,  tables  of  secants  are  omitted,  the 
reciprocal  of  the  cosine  may  be  used  instead. 


Exercise  G-4. 
Use  of  Logarithms. 

References:   Pages  374  to  376,  pages  650  and  718. 

Directions:  1.  Before  beginning  this  exercise  go  through 
the  tables,  p.  719  to  p.  763,  drawing  indices  or  arrows  at  each 
of  the  four  corners  of  every  page  as  indicated  on  p.  375.  2.  On 
a  narrow  strip  of  cardboard  print  two  sets  of  headings  to  fit 
the  tables  as  suggested  in  §  426  (4),  p.  375. 

Problem  25:  1.  Given  a  triangle  ABC  right-angled  at  B. 
A5  =  24'7i";  BC  =  1Q' 4&".  Reduce  the  given  lengths  to 
feet  and  decimals  of  a  foot.  (Use  table  on  p.  650.)  2.  Find 
the  natural  tangent  of  the  angle  CAB.  3.  Find  the  corre- 
sponding value  of  the  angle  CAB.  (Table  XV.)  4.  Find  the 
logarithm  of  the  natural  tangent  obtained  above  in  (2).  (Table 
XVII.)  5.  Look  up  in  the  logarithmic  tables  (XVIII)  the 
logarithmic  tangent  corresponding  to  the  angle  found  in  (3),  and 
compare  this  logarithm  with  the  logarithm  found  in  (4). 


GENERAL  METHODS  OP  COMPUTATION.    115 

Problem  26:  Find  the  logarithms  for  the  following  quantities: 

1.  log.  cos.    98°  12' 

2.  log.  tan.  155°  13' 

3.  log.  sin.  168°  12' 

4.  log.  cot.  109°  43' 

5.  log.  cos.  109°  12'  20" 

6.  log.  tan.    21°  33'  44" 

7.  log.  sin.  123°  14'  32" 

8.  log.  cot.  164°  12'  18" 

Problem  27 ':  Find  the  angles  corresponding  to  the  following 
logarithms :  * 

1.  log.  cos.  A  =    9.918147 

2.  log.  tan.  B  =  10.888449 

3.  log.  cot.  C  =    9.060016 

4.  log.  sin.  D  =    9.987186 

5.  log.  cos.  E  =    9.378321 

6.  log.  tan.  F  =  10.654632 

7.  log.  cot.  G  =    9.685417 

8.  log.  sin.  H  =    9.956666 

Questions:  1.  How  may  time  be  saved  in  logarithmic  com- 
putations? p.  374,  §  426  (1).  2.  Give  some  suggestions  for 
avoiding  mistakes  especially  in  interpolating,  §  426  (2).  What 
are  some  of  the  mistakes  likely  to  be  made  when  an  angle 
is  more  than  90°?  §  426  (3).  4.  When  several  methods  of 
computation  may  be  used  in  finding  angle  or  a  side  of  a  triangle, 
when  would  you  use  tangent  and  cotangents,  and  when  sines 
and  cosines?  p.  376. 

Logarithmic  functions  of  angles  near  0°  and  90°.     See  p.  718. 

Problem  28:  Find  by  the  method  explained  on  p.  718  the  log- 
arithms of: 

1.  log.  sin.     0°  43'  45" 

2.  log.  tan.    0°  38'  15" 

3.  log.  cot.    0°  59'  14" 

4.  log.  cos.  89°  02'  25" 

Find  the  angles  corresponding  to  the  following  logarithms: 

5.  log.  sin.  A  =    8.174231 

6.  log.  tan.  A  =    8.235489 

7.  log.  cot.  A  =  11.984362 

8.  log.  cos.  A  =    8.060753 

*  In  problem  27  the  a-ngle  should  be  expressed  to  the  nearest  second. 
Be  careful  to  observe  the  algebraic  sign  given  for  each  function. 


GROUP   B. 

CALCULATION   OF  BEARINGS. 


Exercise  B-l. 
Calculation  of  Bearings  from  Angles. 

Reference:  Before  beginning  this  exercise  students  should 
study  with  great  care  the  whole  of  Chapter  XXX,  beginning 
on  page  378.  First  learn  to  convert  angular  distance  into  bear- 
ing and  vice  versa,  as  explained  in  §  432,  especially  in  the  note 
at  the  top  of  page  379.  Work  all  the  examples  at  the  top  of 
page  381  before  trying  to  apply  the  method  to  a  system  of 
transit  lines  as  explained  in  §  434. 

Directions:  Follow  the  form  of  computations  given  at  the 
top  of  page  382  and  apply  by  inspection  the  check  of  §  433  (e). 

Problem  29:  1.  Calculate  the  bearings  of  the  transit  lines 
BC,  CD,  and  DA,  p.  179,  assuming  AB  to  be  N.  88°  15'  E. 

30.  Same  as  problem  29,  assuming  the  bearing  of  AB  to  be 
N.  88°  15'  W.  instead  of  N.  88°  15'  E. 

Questions:  1.  Give  the  algebraic  signs  of  bearings  and  angles. 
2.  What  is  meant  by  angular  distance?  3.  Explain  the  gen- 
eral method  of  converting  angular  distance  into  bearing;  of 
bearing  into  angular  distance.  4.  Give  the  general  method 
of  calculating  bearings,  p.  379.  5.  Explain  the  reason  which 
underlies  the  check  of  §  433  (e). 

ADDITIONAL  PROBLEMS. 

Angles  to  the  right.     Calculate  the  bearings  of  the  lines: 

31.  In  the  figure  on  p.  183,  assuming  DA  to  be  N.  80°  30'  E. 

32.  In  the  figure  QRSTY,  p.  390,  assuming  QR  to  be  N.  43° 
10' W. 

33.  In   the   figure   QRSTUVWNOPQ,  p.  390,  assuming  QR 
S.  36°  12'  W. 

116 


CALCULATION    OF    BEARINGS.  117 

Angles  to  the  left.     Calculate  the  bearings  of  the  lines: 

34.  In  the   figure   on   p.  183,  using  the  same  values    as   in 
problem  31  above,  but  going  from  D  to  C  to  B  to  A  (counter- 
clockwise). 

35.  Same  as  problem  32,  but  go  from  Q  to  Y  to  T  to  S  to 
R  (counter-clockwise). 

Angles  to  the  right  or  to  the  left.  Calculate  the  bearings  of 
the  lines:  AB,  BC,  CD,  DE,  EF,  FG,  GH,  HI,  and  IK.  Clock- 
wise =  +  ;  counter-clockwise  =  — .  Use  the  values  of  the  angles 
given  below. 

36.  Line  AB  =  N.  70°  E.;  ABC  =  199°  +  ;  CDB  =  101°  +  ; 
CDE  =71°  -  ;  DEF  =  74°  +  ;   EFG  =  98°  - ;  FGH  =  263°-  ; 
GHI  =  82°  +  ;  HIK  =  300°  +. 

37.  Same  as  problem  36  except  assume  the  bearing  of  AB 
N.  70°  W.  instead  of  N.  70°  E. 

38.  Same  as  problem  36  except  start  with  the  line  EF,  assum- 
ing its  bearing  to  be  N.  5°  E. 

39.  Same  as  problem  38  except  assume  bearing  of  EF  to  be 
S.  5°  E. 

40.  Line    AB  =  S.  80°  E.;      ABC  =  100°    10'  +;     BCD  = 
265°  23'  -  ;    CDE  =  86°  12'-  ;    DEF  =  243°  47'  +  ;    EFG  = 
168°  13'  +  ;  FGH  =  58°  34'  -  ;  GUI  =  38°  21'  -f . 

41.  Same  as  problem  40  except  start  with  EF  whose  bearing 
may  be  assumed  EF  =  N.  70°  E. 

42.  Same  as  problem   41    except   assume   bearing  of  EF  = 

N.  70°  W. 

Deflection  angles.  Calculate  bearings  from  the  following  deflec- 
tion angles  by  the  method  referred  to  on  p.  382,  §  434  (b). 

43.  Line   AB  =  N.    84°   E.;     B  =  36°  R.,    C  =  43°  L.,   D  = 
15°    L.,    E  =  52°  R.,    F  =  87°  L.,    G  =  21°    R.,    H  =  49°    R., 
I  =  17°  L.     Check  the  bearing  of  IJ  by  the  method  outlined  at 
the  bottom  of  p.  155. 

44.  Same  as  problem  43  except  the  bearing  of  A  B  is  N.  84°  W. 

45.  Same  as  problem  43  except  bearing  of  A  B  is  S.  8°  W. 

46.  Same  as  problem  43  except  bearing  of  AB  is  S.  12°  E. 


118  CALCULATION    OF   BEARINGS. 

Exercise  B-2. 

Changing  the  Bearings  of  AH  Lines  of  a  Traverse  by  a 
Given  Amount. 

Reference:  Page  382,  §  343  (c). 

Problem  47:  1.  Assuming  the  bearing  of  QR  on  p.  392  to  be 
S.  44°  26'  E.,  change  the  bearings  of  RS,  ST,  TY,  and  YQ  to 
correspond. 

48.  Assuming  the  bearing  of  QY  on  p.  392  to  be  N.  28°  16'  E., 
change  the  bearings  of  YW,  WO,  OP,  and  PQ  to  correspond. 

ADDITIONAL   PROBLEMS. 

49.  Assume  CD  on  p.  386  to  be  a  north  and  south  line.     Change 
the  bearings  of  DA,  AB,  and  BC  to  correspond. 

50.  Assume  QR  on  p.   392  to   be  a  north  and  south  line. 
Change  the  bearings  of  RS,  ST,  TY,  and  YQ  to  correspond. 

51.  Assume  the  bearing  of   the  line  UV  on    p.    392   to  be 
N.  0°  E.     Change  the  bearings  of  VW,  WN,  NO,  OP,  PQ,  QR,  RS, 
ST,  and  TU  to  correspond. 

52.  The  bearings  of  four  lines  are  given  as  follows:    1-2  = 
S.  5°  26'  W.,  2-3  =  S.  70°  39'  E.,  3-4  =  N.  47°  48'  E.,  4-1  = 
S.  77°  33'  W.     If  the  bearing  of  3-4  is  changed  to  N.  0°  E.,  what 
are  the  corresponding  bearings  of  the  other  three  lines? 


Exercise  B-3. 
Calculation  of  Angles  from  Bearings. 

Reference:  Page  382,  §  435. 

Problem  53:  1.  AB  =  N.  32°  E.,  BC  =  S.  8°  W.,  CD  =  N.  72° 
W.,  DE  =  S.  20°  W.,  EF  =  S.  10°  E.,  FG  =  N.  63°  E.,  GH  = 
S.  0°  E.,  and  HI  =  S.  89°  W.  Find  the  angles  measured  clock- 
wise at  stations  B,  C,  D,  E,  F,  G,  and  H. 

54.  AB  =  S.  70°  W.,  BC  =  S.  0°  21'  E.,  CD  =  S.  86°  14'  E., 
DE  =  S.  46°  43'  W.,  EF  =  S.  90°  W.,  FG  =  N.  12°  37'  E., 
GH  =  N.  44°  12'  W.,  and  HI  =  S.  41°  9'  W.  Find  the  angles 
measured  clockwise  at  B,  C,  D,  E,  F,  G,  and  H. 


CALCULATION    OF   BEARINGS.  119 

ADDITIONAL   PROBLEMS. 

55.  Calculate  the  interior  angles  of  the  polygon  given  in  prob- 
lem 76,  p.  122,*  and  apply  the  closing  check  on  p.  119,  §  175. 

56.  Calculate  the  interior  angles  of  the  polygon  given  in  prob- 
lem 77,  p.  122,*  and  apply  the  closing  check  on  p.  119,  §  175. 

57.  AB  =  S.  0°  E.,  BC  =  S.  42°  18'  E.,  CD  =  N.  88°  14'  E., 
DE  =  N.  15°  47'  W.,  EF  =  N.  90°  W.,  FG  =  S.  38°  58'  W., 
GH  =  N.  87°  17'  W.,  HI  =  N.   12°  11'  E.     Find  the  angles 
measured  clockwise  at  B,  C,  D,  E,  F,  G,  and  H. 

58.  AB  =  N.  89°  12'  E.,  BC  =  N.  20°  19'  W.,  CD  =  S.  81° 
54'  W.,  DE  =  N.  43°  29'  E.,  EF  =  S.  67°  21'  E.,  FG  =  S.  36° 
57'  W.,  GH  =  N.  24°  33'  W.,  HI  =  N.  80°  W.     Find  the  angles 
measured  clockwise  at  B,  C,  D,  E,  F,  G,  and  H. 

59.  Calculate  the  deflection  angles  at  B,  C,  D,  E,  F,  G,  and  H 
from  the  following  bearings:   AB  =  N.  71°  12'  E.,  BC  =  S.  87° 
23'  E.,  CD  =  N.  68°  54'  E.,  DE  =  S.  55°  42'  E.,  EF  =  N.  65° 
24'  E.,  FG  =  N.  1°  22'  W.,  GH  =  N.  43°  E.,  HI  =  N.  20°  18'  W. 
Indicate  by  the  letters  "R"  and  "  L"  which  angles  are  to  the 
right  and  which  are  to  the  left,  and  check  results  by  the  method 
explained  at  the  bottom  of  page  155. 

60.  Calculate  the  deflection  angles  at  B,  C,  D,  E,  F,  G,  and  H 
from  the  following  bearings:  AB  =  S.  83°  09'  W.,  BC  =  N.  89° 
03'  W.,  CD  =  S.  47°  12'  W.,  DE  =  S.  0°  0'  W.,  EF  =  S.  51° 
14'  W.,  FG  =  S.  43°  42'  E.,  GH  =  S.  0°  09'  E.,  HI  =  S.  72° 
53'  W.,  IJ  =  S.  20°  11'  W.     Indicate  by  the  letters  "  R"  and 
"  L"  which  angles  are  to  the  right  and  which  are  to  the   left, 
and  check  results  by  the  method  explained  at  the  bottom  of 
p.  155. 

61.  Calculate  the  deflection  angles  at  stations:  8  +  50, 14  +  30, 
19  +  21,    23  +  72,    28  +  91,    33  +  19,    and    40  +  10.     The 
bearings  of  the  lines  beginning  with  the  line  from  0  to  8+50 
given  in   order  are  as  follows:    S.   80°   10'  E.,   N.  80°  24'  E., 
S.  71°  52'  E.,  S.  1°  11'  E.,  S.  43°  22'  E.,  S.  37°  18'  W.,  S.  86°  04' 
W.,  S.  43°  12'  W.     Indicate  by  the  letters  "  R"  and  "  L"  which 
angles  are  to  the  right  and  which  are  to   the  left,  and  check 
results  by  the  method  explained  at  the  bottom  of  p.  155. 

62.  Calculate    the    deflection    angles    at    stations:     4  +  30, 
8  +  95,  11  +  81,  15  +  20,  19  +  92,  24  +  03,  and  28  +  11.    The 


120        CALCULATION  OF  BEARINGS. 

bearings  of  the  lines  beginning  with  the  line  from  0  to  4  +  30 
given  in  order  are  as  follows:  N.  3°  12'  W.,  N.  42°  19'  W.,  N.  0° 
03'  E.,  N.  88°  58'  W.,  S.  63°  09'  W.,  N.  47°  18'  W.,  N.  0°  V  W., 
N.  71°  21'  W.  Indicate  by  the  letters  "  R"  and  "  L"  which 
angles  are  to  the  right  and  which  are  to  the  left,  and  check 
results  by  the  method  explained  at  the  bottom  of  p.  155. 


GROUP   L. 

LATITUDES   AND   DEPARTURES. 


Exercise  L. 
Calculation  of  Latitudes  and  Departures. 

Reference:  Chapter  XXXI,  pp.  384  to  394. 

Directions:  1.  In  each  problem  make  a  rough  sketch  of  the 
traverse  lines,  placing  the  bearing  and  length  of  each  line  on  the 
sketch,  as  illustrated  on  p.  392.  2.  Rule  five  columns  with 
headings  corresponding  to  those  on  p.  393.  3.  In  the  first 
column  put  down  the  data,  i.e.  the  bearing  and  length  of  each 
line,  also  the  notation  for  the  line,  as  illustrated  in  the  first 
column  on  p.  393.  4.  Look  up  all  the  logarithms,  one  right 
after  the  other,  and  enter  them  in  the  third  and  fourth  columns; 
see  p.  393.  5.  Perform  the  necessary  addition.  6.  Look  up  the 
departures  and  latitudes  corresponding  to  the  logarithms  found 
by  addition,  entering  each  departure  and  each  latitude,  as  soon 
as  found,  in  the  second  and  fifth  columns,  respectively;  see 
p.  393.  7.  Tabulate  the  latitudes  and  departures  as  illustrated 
on  p.  394.  8.  If  the  traverse  is  a  polygon  and  any  large  error 
is  evident  in  the  sums  of  the  latitudes  or  the  departures,  apply 
the  checks  explained  at  the  bottom  of  p.  389. 

Note:  The  above  method  of  procedure  is  practically  the  same  as  that 
given  on  p.  389.  It  will  be  observed  that  like  operations  are  grouped 
(see  p.  364,  §  423),  and  the  student  will  save  time  and  avoid  mistakes  if 
he  will  follow  closely  the  method  of  procedure  indicated. 

Problems:  (To  be  assigned  from  the  sixteen  problems 

given  below.) 

Remark:  The  latitudes  and  departures  computed  in  any  problem  of  th,s 
exercise  may  be  used  in  a  subsequent  exercise  requiring  the  calculation  of 
omitted  measurements  or  the  area  of  a  polygon.  Problems  75,  76  and  77 
are  used  in  this  way  repeatedly  in  succeeding  exercises,  while  occasional 
use  is  made  of  Problems  71,  72..  73,  74  and  78.  It  will  save  time  in  the  end, 
therefore,  to  assign  as  many  of  the  problems  given  below  as  possible,  even 
though  it  may  seem  that  a  disproportionate  amount  of  time  is  being  given 
to  the  mere  calculation  of  latitudes  and  departures. 

When  the  student  has  learned  to  compute  latitudes  and  departures 
by  means  of  logarithms,  he  may  be  given  practice  in  solving  some  of  the 
problems  by  the  use  of  traverse  tables.  See  p.  387,  §  444  (b).  He  may 
also  be  given  practice  in  the  construction  and  use  of  a  trigonometer.  (See 
p.  388.) 

121 


122  LATITUDES   AND   DEPARTURES. 

PROBLEMS. 

71.  Calculate  the  latitudes  and  departures  of  the  transit  lines 
A  BCD,  p.  179. 

72.  Calculate  the  latitudes  and  departures  of  the  transit  lines 
ABCD,  p.  183. 

73.  AB  =  N.  25°  16'  E.,  150.0  ft.;  BC  =  S.  59°  54'  E.,  210.0 
ft.;    CD  =  S.   19°  28'  W.,   285.5  ft.;    DA  =  N.   32°  14'  W., 
282.3  ft.     Calculate  and  tabulate  latitudes  and  departures. 

74.  AB  =  N.  26°  30'  E.,  547.3  ft.;  BC  =  S.  78°  18'  E.,  504.8 
ft.;   CD  =  S.  9°  01'  E.,  315.5  ft.;  DA  =  S.  84°  30'  W.,  791.6  ft. 
Calculate  and  tabulate  latitudes  and  departures. 

75.  AB  =  S.  43°  16'  W.,  206.6  ft.;   BC  =  S.  12°  43' E.,  196.6 
ft.;   CD  =  S.  83°  45'  E.,  530.9  ft.;   DE  =  N.  3°  13'  W.,  896.7 
ft.;  EA  =  S.  37°  26'  W.,  623.7  ft.     Calculate  and  tabulate  lati- 
tudes and  departures. 

76.  AB  =  N.  60°  15'  E.,  432.6  ft.;  BC  =  S.  70°  10'  E.,  310.8 
ft. ;  CD  =  S.  35°  30'  W.,  290.5  ft. ;  DE  =  N.  65°  05'  W.,  168.2 
ft.;    EA  =  N.  80°  47'  W.,  351.3  ft.     Calculate  and  tabulate 
latitudes  and  departures. 

77.  1-2  =  S.  73°  21'  E.,  247.2  ft. ;  2-3  =  S.  40°  10'  E.,  154.3 
ft.;    3-4  =  S.  26°  42'  W.,  611.9  ft.;    4-5  =  N.   14°  20'  W., 

483.5  ft. ;  5-1  =  N.  12°  20'  E.,  273.3  ft.     Calculate  and  tabulate 
latitudes  and  departures. 

78.  Assume  the  bearing  of  the  line  RS,  p.  392,  to  be  S.  0°  0'  E. 
Change  the  bearings  of  ST,  TU,  UV,  VW,  WN,  NO,  OP,  PQ, 
and  QR  to  correspond.     Calculate  and  tabulate  the  latitudes 
and  departures  of  the  perimeter  of  the  figure,  i.e.,  the  polygon 
RSTUVWNOPQ. 

79.  Same  as  problem  78  except  assume  the  line  UV  to  be  a 
north  and  south  line,   and  change  the  bearings  of  the  other 
nine  lines  to  correspond. 

80.  1-2  =  N.  7°  54'  E.,  483.4  ft.;    2-3  =  N.  86°  46'  W., 

380.6  ft.;    3-4  =  S.  9°  38'  W.,  225.9  ft.;    4-5  =  S.  20°  10'  E., 
241.9  ft.;    5-1  =  S.  79°  18'  E.,  272.7  ft.     Calculate  and  tabu- 
late latitudes  and  departures. 

81.  AB  =  N.  50°  55'  W.,  449.3  ft.;    BC  =  N.   1°  19'  W., 
337.8  ft.;   CD  =  N.  87°  38'  E.,  264.9  ft.;   DE  =  S.  38°  50'  E., 
205.2  ft.;    EF  =  S.  34°  50'  W.,  120.5  ft.;   FA  =  S.  4°  54'  E., 

374.7  ft.     Calculate  and  tabulate  latitudes  and  departures. 


LATITUDES   AND   DEPARTURES.  123 

J     82.   AB  =  N.  2°  05'  W.,   183.5  ft.;    BC  =  N.  57°  40'  W., 

273.3  ft. ;  CD  =  S.  42°  25'  30"  W.,  639.4  ft. ;  DE  =  S.  71°  18'  E., 

598.4  ft.;   EF  =  S.  89°  37'  E.,  340.0  ft.;  FA  =  N.  35°  14'  W., 
412.2  ft.     Calculate  and  tabulate  latitudes  and  departures. 

83.   AB  =  N.  56°  36'  W.,  279.0  ft.;    BC  =  S.  44°  02'  W., 


286.0  ft. 

174.1  ft. 
445.6  ft. 


CD  =  S.  25°  00'  W.,  171.8  ft.;  DE  =  S.  40°  39'  W., 
EF  =  S.  71°  30'  E.,  442.4  ft.;  FG  =  S.  87°  37'  E., 
GH  =  N.  41°  07'  W.,  402.8  ft.;  HA  =  N.  5°  11'  E., 


195.8  ft.     Calculate  and  tabulate  latitudes  and  departures. 

Problems  in  calculating  latitudes  and  departures  from  azimuth 
(reckoned  clockwise  from  the  north).  Problems  84  and  85  are 
rough  surveys  and  the  error  of  closure  should  be  corrected  by  the 
first  method  of  balancing  a  survey  explained  on  p.  395^ 

84.  AB  =  32°  28',  334  ft.;  BC  =  20°  34',  308  ft.;  CD  = 
239°  02',  228  ft. ;  DE  =  219°  50',  183  ft.;  EA  =  175°  00',  310  ft.; 
Calculate  and  tabulate  latitudes  and  departures  and  balance 
the  survey. 

v  85.  AB  =  18°  11',  450  ft.;  BC  =  355°  00',  310  ft.;  CD  = 
322°  46',  200  ft. ;  DE  =  221°  10',  460  ft. ;  EF  =  152°  00',  230  ft. ; 
FG  =  123°  14',  281  ft.;  GA  =  189°  03',  195  ft.  Calculate  and 
tabulate  latitudes  and  departures  and  balance  the  survey. 

86.    Change   all   the   bearings   in   problem  to   azimuths, 

but  retain  the  same  lengths.  Calculate  and  tabulate  latitudes 
and  departures.  (The  number  of  the  problem  to  be  inserted  in 
the  blank  space  will  be  assigned  by  the  instructor  from  among  the 
first  thirteen  problems  given  above.) 

Note:  An  indefinite  number  of  problems  may  be  arranged  by  changing 
all  the  bearings  in  any  one  of  the  above  problems  by  a  given  amount,  as 
for  example,  by  30°  +  or  40°  —  and  so  on. 

Questions:  *  1.  What  is  meant  by  the  term  latitude ;  departure? 
2.  Explain  how  each  is  found  from  the  bearing  and  length  of  a 
line.  3.  What  are  the  algebraic  signs  for  the  different  quad- 
rants of  bearings?  4.  What  is  the  departure  of  any  north  and 
south  line,  and  the  latitude  of  any  east  and  west  line?  5.  Ex- 
plain by  means  of  a  sketch  how  latitudes  and  departures  may  be 
used  for  determining  the  position  of  any  station  with  respect  to 
any  other  station  in  a  system  of  transit  lines,  p.  385.  6.  How 
may  the  error  of  closure  be  ascertained?  p.  386.  7.  For  ordinary 

*  Many  of  the  explanations  involved  in  the  answer  to  these  questions 
should  be  illustrated  by  sketches  at  the  black-board. 


124  LATITUDES    AND   DEPARTURES. 

transit  work  what  are  the  permissible  errors  of  closure?  p.  160. 

8.  Suppose  that  the  permissible  error  for  one  angle  is  30"  and 
that  the  total  length  of  the  perimeter  of  a  sixteen-sided  polygon 
is  5000  ft.     What  is  the  limit  for  the  error  of  closure?  p.   161. 

9.  Every  line  has  two  bearings.     Which  is  used  in   computing 
latitudes  and  departures?  p.  387.     10.    Explain  how  to  compute 
latitudes  and  departures  from  azimuths,  p.  387.     11.  Explain  the 
use  of  traverse  tables.     12.    Explain  the  construction  and  use 
of  a  trigonometer.     13.    Illustrate  by  sketch  how  the  true  bear- 
ings of  traverse  lines  may  be  obtained  by  observation  on  Polaris, 
p.  389,  §  445  (3).     14.    How  could  true  bearings  be  obtained 
from  the  magnetic  bearings  if  the  magnetic  declination  is  known? 
p.  389,  Remark.     15.    So  far  as  plotting  is  concerned,  does  it 
make  any  difference  what  value  is  taken  for  the  bearing  of  the 
first  line  if  the  bearings  of  the  other  lines  are  calculated  from  that 
bearing?     16.    When  the  sums  of  the  latitudes  or  the  sums  of 
the  departures  are  not  equal  within  the  limit  of  error,  what  three 
checks  would  you  apply?     (Bottom  of  p.  389.) 

Questions  on  balancing  survey:  1.  What  is  meant  by  balancing 
survey?  p.  395.  2.  Is  it  usually  necessary  to  balance  a  survey 
for  purposes  of  plotting?  3.  When  is  it  necessary  to  balance  a 
survey?  4.  What  two  general  methods  are  used  for  balancing 
a  survey?  p.  395.  5.  Explain  the  first  method.  6.  What 
effect  has  the  balancing  of  a  survey  on  the  original  bearings  and 
lengths?  p.  396,  Note.  7.  How  may  the  original  bearings  and 
lengths  be  corrected?  8.  Explain  the  second  method  of  balanc- 
ing a  survey  (p.  396):  (1)  Measurements  made  under  unfavor- 
able conditions.  (2)  Linear  measurements  likely  to  be  too  long, 
which  quantities  should  be  decreased.  (3)  Effect  of  changes  of 
long  and  short  lines.  (4)  Effect  of  changes  in  north  and  south 
lines,  and  east  and  west  lines.  9.  Give  the  substance  of  Mr. 
Gould's  discussion,  p.  397. 


GROUP   T. 

TRIANGULATION. 


Exercise  T-l. 
Computations  for  Triangulations. 

Reference:  Page  399,  §  488. 

Directions:  Find  by  calculation  the  lengths  of  the  side  of  each 
triangle  in  a  triangulation  net,  using  the  form  shown  on  p.  400, 
§  448  (d).  The  student  should  prepare  the  above  form  for  each 
triangle  before  looking  up  logarithms. 

Problems:  (To    be    assigned   from,  the   problems   given 

below.) 

PROBLEMS. 

101.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  BA  =  1070.06  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  ABC  Triangle  A  CD  Triangle  ADE 

BAG  =  82°  16'  27"  CAD  =  39°  16'  II"  DAE  =  63°  38'  48" 
ACB  =  57°  12'  03"  ADC  =  100°  42'  14"  A  ED  =  49°  27'  10" 
ABC  =  40°  31'  30"  DC  A  =  40°  01'  35"  EDA  =  66°  54'  02" 

102.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  BA  =  1421.36  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  A  EC  Triangle  BCD  Triangle  CDE 

ABC  =  64°  48'  41"  BCD  =  60°  21'  18"  CDE  =  67°  12'  42" 
BAG  =  61°  21'  14"  CBD  =  80°  24'  28"  DCE  =  63°  16'  20" 
ACB  =  53°  50'  05"  BDC  =  39°  14'  14"  CED  =  49°  30'  58" 

103.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  AB  =  2121.83  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  A  BC  Triangle  A  CE  Triangle  CBD 

ABC  =  55°  10'  20"      ACE  =  46°  42'  20"  CBD  =  82°  51'  11" 

BAG  =  54°  48'  15"      CAE  =  88°  51'  12"  BCD  =  41°  19'  04" 

ACB  =  70°  01'  25"      AEG  =  44°  26'  28"  CDS  =  55°  49'  45" 

125 


126  TRIANGULATION. 

104.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  BD  =  2421.16  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  BDC             .  Triangle  BCA  Triangle  DCE 

BDC  =  70°  00'  45"  BCA  =  49°  10'  15"  DCE  =  61°  24'  10" 

DEC  =  56°  49'  04"  CBA  =  58°  36'  30"  CDE  =  60°  28'  14" 

BCD  =  53°  10'  11"  BAG  =  72°  13'  15"  DEC  =  58°  07'  36" 

105.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  XY  =  3121.42  ft.      Adjusted  values  of  the  angles  are 
given  below. 

Triangle  XYW  Triangle  XWU  Triangle  YWV 

XYW  =  61°  22'  44"  XWU  =  59°  18'  40"  YWV  =  80°  09'  10" 

YXW  =  58°  21'  10"  WXU  =  63°  12'  10"  WYV  =  40°  12'  14" 

XWY  =  60°  16'  06"  XUW  =  57°  29'  10"  YVW  =  59°  38'  36" 

106.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  RS  =  432.461  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  RST  Triangle  RTU  Triangle  STV 

RST  =  40°  21'  40"  RTU  =  38°  18'  47"  STV  =  94°  51'  07" 

SRT  =  55°  39'  15"  TRU  =  93°  44'  21"  TSV  =  44°  06'  41" 

RTS  =  83°  59'  05"  RUT  =  47°  56'  52"  SVT  =  41°  02'  12" 

107.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  1-2  =  496.831  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  1-2-3  Triangle  1-2-5  Triangle  2-3-4 

1-2-3  =    37°  18'  43"  1-2-5  =  43°  18'  47"  2-3-4  =  61°  21'  18" 

2-1-3  =    36°  21'  48"  2-1-5  =  41°  48'  03"  3-2-4  =  58°  53'  12" 

1-3-2  =  106°  19'  29"  1-5-2  =  94°  53'  10"  2-4-3  =  59°  45'  30" 

108.  A  triangulation  net  is  composed  of  three  triangles.     The 
base  line  1-2  =  468.432  ft.     Adjusted  values  of  the  angles  are 
given  below. 

Triangle  1-2-3  Triangle  1-3-4  Triangle  3-4-5 

1-2-3  =  92°  24'  51"  1-3-4  =  41°  02'  11"  3-4-5  =  40°  08'  48" 

2-1-3  =  41°  52'  21"  3-1-4  =  44°  53'  17"  4-3-5  =  41°  37'  44" 

1-3-2  =  45°  42'  48"  1-4-3  =  94°  04'  32"  3-5-4  =  98°  13'  28" 


TRIANGULATION.  127 

Exercise  T-2. 
Miscellaneous  Problems  in  Triangulation. 

109.  In  Fig.  277  (e),  p.  223,  the  length  of  the  base-line  CD  is 
423.738  ft.    ACD  =  109°  11'  30",  BCD  =  43°  42'  12",  ADC  =  33° 
18'  24",  BDC  =  66°  28'  20".     Compute  the  length  of  AB. 

110.  In  Fig.  277  (f),  p.  223,  in  order  to  find  the  distance  AC  a 
base  line  AE  was  laid  off  and  its  length  found  to  be  231.763  ft. 
CAE  =  36°  19'  36",  CEA  =  81°  54'  10".     The  vertical   angle 
CAB  =  21°  18'  40".     The  level  line  AC  strikes  the  building  four 
feet  above    a  point   on  the  ground.     How  high   is  the  point 
B  above  the  same  point  on  the  ground? 

111.  In  the  figure  on  p.  217  the  length  of  base  line  No.  1  is 
879.453,  and  that  of  base  line  No.  2  is  943.768  ft.     NHS  =38° 
21'  40",  HNS  =  37°  10'  5",  HSN  =  104°  28'  15";  MSN  =  68° 
30'  42",  SMN  =  62°  57'  45",  MNS  =  48°  31'  33."     Make  all  of 
the  computations  that  are  necessary  for  locating  Piers  A  and  B, 
assuming  that  the  three  spans  are  equal. 


GROUP  0. 

OMITTED   MEASUREMENTS. 


Exercise  O-l. 

To  Calculate  the  Bearing  and  Length  of  an  Omitted 
Side  of  a  Polygon. 

Reference:  Pages  400  to  402,  Case  I. 

Directions:    Follow  the  method   of  procedure  given  at  the 
bottom  of  p.  401. 

Problem:         (To  be  assigned  from  the  fourteen  problems  given 

below.) 

PROBLEMS. 


Note:   In  the  first  six  problems  the  student  may  use  latitudes  and  depar- 

tures which  he  may  have  already  calculated  in  the  examples 

on  p.  122.* 

In  each  problem  there  will  be  two  solutions,  the  first  from  the 

lines  of  the 

polygon  on  one  side  of  the  missing  line,  the  second  from  the 

lines  of  the 

polygon   on    the   other  side  of    the   missing  line.     If  there  is 

no  error  of 

closure  the  results  should  be  the  same. 

Find  the  length  and  bearing  of  the  line 

121.    From  D  to  A  in  Problem  75,  p.  122.* 

122.    From  B  to  E  in  Problem  76,  p.  122.* 

123.    From  3  to  5  in  Problem  77,  p.  122.* 

124.    From  V  to  P  in  Problem  78,  p.  122.* 

125.    From  0  to  Q  in  Problem  79,  p.  122.* 

126.    From  E  to  H  in  Problem  83,  p    123.* 

127.  Line              Bearing           Length       Latitude 

Departure 

MN        S.  47°  03'  W.        291.7           198.7 

213.6 

NO         N.  43°  55'  W         251.4           181.1 

174.4 

OP          N.  14°  57'  E.         346.4           334.1 

89.2 

PQ          N.  26°  12'  E.         250.7          224.9 

110.7 

Find  the  bearing  and  length  of  the  line  QM. 

128.  Line         Bearing               Length         Latitude 

Departure 

MN    N.  47°  48'  E.      1000.6    ft.        672.14 

741.26 

NO      N.  62°  38'  W.       573.29  ft.        263.53 

509.13 

OP      S.   76°  40'  W.       330.33  ft.          76.18 

321.42 

PQ      S.     5°  26'  W.       804.99  ft.        801.38 

76.23 

Find  the  bearing  and  length  of  the  line  QM. 

128 


OMITTED   MEASUREMENTS.  129 

129.  EA  =  N.  65°  05'  E.,  804.6  ft. ;  AB  =  S.  50°  20'  E.,  370.5 ft.; 
BC  =  S.  25°  16'  W.,  315.8  ft.;  CD  =  S.  45°  31'  W.,  291.6  ft. 
Find  the  bearing  and  length  of  DE. 

130.  GC  =  N.  84°  27'  W.,  268.5  ft.;  CD  =  N.  31°  53'  W., 
337.2  ft.;  DE  =  N.  30°  11'  E.,  263.9  ft.;  EF  =  S.  65°  10'  E., 

310.6  ft.     Find  the  bearing  and  length  of  FG. 

131.  1-2  =  N.  41°  48'  E.,  212.4  ft.;  2-3  =  S.  68°  19' E.,  411.3 
ft.;  3-4  =  S.  3°  51'  E.,  394.7  ft.;  4-5  =  S.  36°  10'  W.,  381.6  ft. 
Find  the  bearing  and  length  of  5-1. 

132.  1-2  =  N.  46°  18'  W.,  321.6  ft.;  2-3  =  S.  48°  59'  W., 

401.7  ft.;  3-4  =  S.  0°  49'  E.,  372.1  ft.;  4-5  =  S.  8°  09'  E., 

241.8  ft.     Find  the  bearing  and  length  of  5-1. 

133.  In  Problem  107,  p.  126,*  assume  that  the  angles  3-2-4 
and  2-4-3  are  not  known,  but  that  all  the  other  angles  are  as  given 
in  that  problem,    (a)  Assume  the  bearing  of  4-3  to  be  any  value 
you  please,  and  from  this  bearing  compute  the  bearings  of  3-1, 
1-5,  and  5-2  by  the  method  of  Chapter  XXX,  using  angles 
4-3-1,  3-1-5,  and  1-5-2.     (6)  Using  these  bearings  and  the 
lengths  of  4-3,  3-1,  1-5,  and  5-2   (found  by  computation  in 
Exercise  T-l),  compute  the  latitudes  and  departures  of  these 
four  lines,     (c)  From  these  latitudes  and  departures  compute 
the  length  and  bearing  of  the  line  2-4.     (d)  Compare  this  length 
of  2-4  with  the  length  found  in  the  triangulation  computation. 
(e)  From  the  bearings  of  4-3  and  4-2  find  the  angle  3-4-2  and 
compare  its  value  with  the  value  of  3-4-2  given  in  Problem  107, 
p.  126.* 

134.  A  problem  similar  to  Problem  133  made  up  from  one  of 
the  triangulation  problems  on  p.  125  or  126.* 

Exercise  O-2. 

To  Calculate  the  Omitted  Bearing  of  One  Side  and  the 
Omitted  Length  of  Another  Side  of  a  Polygon. 

'  Reference:  Page  403,  Case  II. 

Directions:  Problems  under  Case  II  may  be  solved  by  two 
methods.  In  each  of  the  problems  given  below  follow  that  order 
of  procedure  on  p.  403  which  corresponds  to  the  method  called 
for  in  the  problem.  Notice  the  Remark,  p.  403. 

Problem:  (To  be  assigned  from  the  seventeen  problems 
given  below.) 


130  OMITTED   MEASUREMENTS. 

PROBLEMS. 

Note:  In  each  of  the  first  seven  problems  the  student  may  use  the  lati- 
tudes and  departures  which  he  may  have  already  calculated  in  the  corre- 
sponding problem  on  p.  122,*  except,  of  course,  the  latitude  and  departure 
of  a  side  whose  bearing  or  length  is  assumed  to  be  omitted. 

141.  In  Problem  75,  p.  122,*  assume  the  bearing  of  DE  and 
the  length  of  EA  to  be  omitted.     Calculate  the  omitted  meas- 
urements by  the  first  method  of  Case  II,  p.  403. 

142.  Same  as  Problem  141  except  use  the  second  method  of 
Case  II,  p.  403. 

143.  In  Problem  76,  p.  122,*  assume  the  bearing  of  BC  and 
the  length  of  CD  to  be  omitted.     Calculate  the  omitted  meas- 
urements by  the  first  method  of  Case  II,  p.  403. 

144.  Same  as  Problem  143  except  use  the  second  method  of 
Case  II,  p.  403. 

145.  In  Problem  77,  p.  122,*  assume  the  bearing  of  3-4  and 
the  length  of  4-5  to  be  omitted.     Calculate  the  omitted  measure- 
ments by  the  first  method  of  Case  II,  p.  403. 

146.  Same  as  Problem  145  except  use  the  second  method  of 
Case  II,  p.  403. 

147.  A  problem  similar  to  the  above  problems  made  up  from 
one  of  the  problems  on  p.  122,  123,  125  or  126.* 

148.  CD  =  S.   47°  29'  W.,  562.3  ft.;  DA  =  N.  50°  15'  W., 
380.4  ft.;  AB  =  S.  65°  27'  E.;  BC  =  435.2  ft.     Calculate  the 
bearing  of  BC  and  the  length  of  AB.     Use  the  first  method  of 
Case  II  and  check  by  the  second  method. 

149.  AB  =  N.  73°  58'  W.,  125.5  ft.;  BC  =  S.  8°  48'  E.,  163.9  ft.; 
CD  =  87.5  ft. ;  DA  =  N.  5°  40'  W.     Calculate  the  bearing  of  CD 
and  the  length  of  DA.     Use  the  first  method  of  Case  II  and  check 
by  the  second  method. 

150.  AB  =  N.   40°  2J)'   E.,   302.6  ft.;   BC  =  N.  71°  15'  E., 
282.2  ft.;  CD  =  S.  50°  10'  E.;  DE  =  S.  45°  25'  W.,  510.6  ft.; 
EA  =  466.3  ft.     Calculate  the  bearing  of  EA  and  the  length  of 
CD,  using  the  second  method  of  Case  II. 

151.  Same  as  Problem  150,  using  the  first  method  of  Case  II. 

152.  AB  =  N.  40°  00'  E.,  530.2  ft.;  BC  =  S.  60°  20'  E.,  421.6 
ft.;  CD  =  527 A  ft.;  DE  =  S.  65°  10'  W.;  EA  =  N.  35°  10'  W., 
578.6  ft.     Calculate  the  bearing  of  CD  and  length  of  DE,  using 
the  first  method  of  Case  II. 


OMITTED   MEASUREMENTS.  131 

153.  Same   as  Problem   151,   using  the  second    method    of 
Case  II. 

154.  (In  this  problem  the  omitted  measurements  affect  sides 
which  are  not  adjacent.)     AB  =  N.  46°  05'  E.,  433.4  ft.;  BC  = 
S.  62°  50'  E.,  183.6  ft.;  CD  =  S.  27°  28'  E.,  402.7  ft.;  DE  = 
S.   39°   48'   W.;   EF  =  52°  07'  W.,   323.6  ft.;  FA  =  298.6  ft. 
Calculate  the  bearing  of  FA  and  the  length  of  DE,  using  the 
second  method  of  Case  II. 

155.  Same  as  Problem  154,  using  first  method  of  Case  II. 

156.  AB  =  N.  32°  05'  E.,  263.2  ft.;  BC  =  N.  74°  18'  E.,  234.4 
ft.;  CD  =  S.  12°  52'  W.,  465.3  ft.;  DE  =  525.0  ft.;  EA  =  S.  62° 
27'  W.     Calculate  the  bearing  of  DE  and  the  length  of  EA,  using 
the  first  method  of  Case  II. 

157.  Same    as    Problem    156,   using  the  second   method  of 
Case  II. 


Exercise  O-3. 

To  Calculate  the  Omitted  Lengths  of  Two  Sides 
of  a  Polygon. 

Reference:  Page  404,  Case  III. 

Directions:  Problems  under  Case  III  may  be  solved  by  two 
methods.  In  each  of  the  problems  given  below  follow  that  order 
of  procedure  on  p.  404,  which  corresponds  to  the  method  called 
for  in  the  problem.  Notice  the  "  Remark  "  on  p.  404. 

Problem:  (To  be  assigned  from  the  fourteen  problems 

given  below.) 

PROBLEMS. 

Note:  In  each  of  the  first  seven  problems  the  student  may  use  the  lati- 
tudes and  departures  which  he  may  have  already  calculated  in  the  corre- 
sponding problem  on  p.  122,*  except,  of  course,  the  latitude  and  departure 
of  a  side  whose  length  is  assumed  to  be  omitted. 

171.  In  Problem  75,  p.  122,*  assume  the  lengths  of  BC  and  CD 
to  be  omitted.     Calculate  the  omitted  measurements  by  the  first 
method  of  Case  III,  p.  404. 

172.  Same  as  Problem  171  except  use  the  second  method  of  Case 
III,  p.  404. 


132  OMITTED   MEASUREMENTS. 

173.  In  Problem  76,  p.  122,*  assume  the  lengths  of  BC  and  CD 
to  be  omitted.     Calculate  the  omitted  measurements  by  the  first 
method  of  Case  III,  p.  404. 

174.  Same  as  Problem  173  except  use  the  second  method  of 
Case  III,  p.  404. 

175.  In  Problem  77,  p.  122,*  assume  the  lengths  of  2-3  and  4-5 
to  be  omitted.     Calculate  the  omitted  measurements  by  the  first 
method  of  Case  III,  p.  404. 

176.  Same  as  Problem  175  except  use  the  second  method  of 
Case  III,  p.  404. 

177.  A  problem  similar  to  the  above  problems,  made  up  from 
one  of  the  problems  on  p.  122,  123,  125  or  126.* 

178.  AB  =  N.  68°  11'  W.,  216.0  ft.;  BC  =  S.  33°  35'  W.,  167.0 
ft.;  CD  =  S.  32°  27'  E.;  DA  =  N.  41°  59'  E.     Calculate  the 
lengths  of  CD  and  DA.     Use  the  first  method  of  Case  III,  and 
check  by  the  second  method. 

179.  AB  =  N.  16°  42'  E.,  273.0  ft.;  BC  =  S.  68°  23'  W.,  388.5 
ft.;  CD  =  S.  10°  12'  E.;  DA  =  N.  50°  46'  E.     Calculate  the 
lengths  of  CD  and  DA.     Use  the  first  method  of  Case  III,  and 
check  by  the  second  method. 

180.  AB  =  N.  36°  30'  E.,  608.1  ft.;  BC  =  S.  68°  18'  E.,  560.9 
ft.;  CD  =  N.  0°  59'  E.;  DA  =  S.  85°  30'  E.     Calculate  the 
lengths  of  CD  and  DA.     Use  the  first  method  of  Case  III,  and 
check  by  the  second  method. 

181.  AB  =  N.  10°  20'  W.,  248.3  ft.;  BC  =  N.  62°  18'  E., 
324.6  ft. ;  CD  =  S.  74°  27'  E. ;  DE  =  S.  20°  22'  W. ;  EA  =  S.  68° 
50'  W.,  463.5  ft.     Calculate  the  lengths  of  CD  and  DE,  using  the 
second  method  of  Case  III. 

182.  Same  as  Problem  181,  using  the  first  method  of  Case  III. 

183.  (In  this  problem  the  omitted  measurements  affect  sides 
which  are  not  adjacent.)     AB  =  S.  70°  05'  W.,  437.9  ft.;  BC  = 
N.  15°  54'  W. ;  CD  =  N.  38°  16'  E.,  217.6  ft.  ;DE  =  S.  10°  02'  W. ; 
EA  =  S.  72°  25'  E.,  366.4  ft.     Calculate  the  lengths  of  BC  and 
DE,  using  the  second  method  of  Case  III. 

184.  Same  as  Problem  183,  using  the  first  method  of  Case  III. 


OMITTED   MEASUREMENTS.  133 


Exercise  O-4. 

To  Calculate  the  Omitted  Bearings  of  Two  Sides  of  a 
Polygon. 

Reference:  Page  404,  Case  IV. 

Directions:  Follow  the  method  of  procedure  of  Case  IV,  p.  404. 
Notice  the  "Remark  "  under  this  case. 

Problem:  .  (To  be  assigned  from  the  nine  problems  given 
below.) 

PROBLEMS. 

Note:  In  each  of  the  first  four  problems  the  student  may  use  the  lati- 
tudes and  departures  which  he  may  have  already  calculated  in  the  corre- 
sponding problems  on  p.  122,*  except,  of  course,  the  latitude  and  departure 
of  a  side  whose  bearing  is  assumed  to  be  omitted. 

191.  In  Problem  75,  p.  122,*  assume  the  bearings  of  BC  and 
CD  to  be  omitted.     Calculate  the  omitted  measurements  by 
the  method  of  Case  IV,  p.  404. 

192.  In  Problem  76,  p.  122,*  assume  the  bearing  of  BC  and 
CD  to  be  omitted.     Calculate  the  omitted  measurements  by  the 
method  of  Case  IV,  p.  404. 

193.  In  Problem  77,  p.  122,*  assume  the  bearings  of  2-3  and 
3-4  to  be  omitted.     Calculate  the  omitted  measurements  by  the 
method  of  Case  IV,  p.  404. 

194.  A  problem  similar  to  the  above  problems,  made  up  from 
one  of  the  problems  on  p.  122,  123,  125  or  126.* 

195.  AB  =  N.  53°  56'  W.,  296.4  ft.;  BC  =  S.  21°  53'  W., 

338.7  ft.;  CD  =  301.0  ft.;  DA  =  406.8  ft.    Calculate  the  bear- 
ings of  CD  and  DA. 

196.  BC  =  S.  41°  45'  W.,  279.8  ft. ;  CD  =  N.  22°  14'  W.,  286.4 
ft.;    DA  =  194.2  ft.;    AB  =  254.5  ft.     Calculate  the  bearings 
of  AB  and  DA. 

197.  AB  =  172.2   ft.;   BC  =  257.5  ft.;   CD  =  S.  63°  37'  E., 

298.8  ft.;   DA  =  N.  13°  25'  W.,  261.6  ft.     Calculate  the  bear- 
ings of  AB  and  BC. 

198.  (In  this  problem  the  omitted  measurements  affect  sides 
which  are  not  adjacent.)     AB  =  N.  38°  40'  E.,  340.5  ft. ;  BC  = 
S.  67°  07'  E.,  527.7  ft.;   CD  =  272.3  ft.;  DE  =  S.  84°  44'  W. 
669.6  ft. ;  EA  =  265.2  ft.     Calculate  the  bearings  of  CD  and  EA. 


134  OMITTED   MEASUREMENTS. 

199.  AB  =  Latitude  234.5  ft.  N.,  departure  181.4  ft.  E.; 
BC  =  Latitude  105.3  ft.  N.,  departure  356.4  ft.  E.;  CD  = 
Latitude  262.1  ft.  S.,  departure  179.4  ft.  E.;  DE  =  385.6  ft.; 
EA  =  532.2  ft.  Find  the  lengths  of  AB,  BC,  and  CD,  and  the 
bearings  of  DE  and  EA. 

Exercise  O-5. 
Calculation  of  Omitted  Measurements. 

Miscellaneous  Problems. 

211.  In  the  figure  on  p.  405,  let  the  distances  Aa  =  49.3  ft., 
Bb  =  28.2  ft.,  Cc  =  33.4  ft.,  and  Dd  =  24.4  ft.     Angles  Aab  = 
90°  23',    cdD  =  102°    10'.     Find  the  bearings  and  lengths  of 
AB,  BC,  and  CD.     (See  p.  406.) 

212.  In  the  figure  on  p.  177,  assume  the  bearing  of  BC  = 
N.  9°  15'  E.     (1)  From  the  notes  on  p.  176,  calculate  the  bear- 
ings of  A B,  BC,  CD,  and  DA,  and  also  the  bearing  of  the  line  from 
each  station  to  the  nearest  corner.     (2)  By  the  method  of  Case  I, 
p    401,  calculate  in  order  the  bearings  and  lengths  of  the  lines 
1-2,  2-3,  3-4,  and  4-1.     (See  illustration,  p.  402,  §  451  (c.)) 

213.  Same  as  Problem  212  except  use  the  method  illustrated 
on  p.  406. 

214.  By  the  method  of  Case  I,  p.  401,  calculate  the  bearings 
and  lengths  of  the  three  fence  lines  on  p.  183. 

215.  Same  as  Problem  214  except  use  the  method  illustrated 
on  p.  406. 

Problems  in  Mine  Surveying. 

216.  A  vertical  shaft  of  a  mine  is  located  at  a  point  A  and 
another  at  a  point  E.     A  point  E'  is  at  the  bottom  of  the  shaft 
directly  under  E.     An  underground  traverse  is  run  from  E'  end- 
ing at  a  point  A'  directly  under  A.     The  bearing  of  E'F'  was 
o,ssumed  as  S.  89°  05'  E.     The  other  values  are  as  follows:  E'F'= 
294.76  ft.;  F'G'  =  S.  89°  22'  E.;  322.4  ft.;  G'H'  =  N.  15°  59'  E., 
710  ft.;    H'P  =  N.  15°  06'  W.,  390.3  ft.;  PA'  =  N.  63°  03'  W., 
259.5  ft.     Afterward  a  traverse  was  run  on  the  surface  of  the 
ground   as  follows:  AB  =  636.43  ft.;  ABC  =  100°  49',   BC  = 
624.34  ft.;  BCD  =  180°  41',  CD  =  218.66  ft.;  CDE  =  148°  23', 
DE  =  239.45  ft.    All  angles  were  measured  clockwise.    The  true 


OMITTED   MEASUREMENTS.  135 

bearing  of  ABwas  determined  as  S.  44°  18'  W.  It  is  required  to 
correct  the  assumed  bearings  of  the  underground  survey  so  that 
they  will  be  true  bearings. 

Note:  As  far  as  possible  the  logarithmic  values  on  p.  393  may  be  used  in 
the  above  example. 

217.  A  traverse  is  run  on  the  surface  of  the  ground  as  follows: 
AB  =  S.  41°  22'  E.,  281.1  ft.;  ABC  =  110°  45',  EC  =  240.8  ft.; 
BCD  =  124°  30',    CD  =  339.7  ft.     Angles  measured  clockwise. 
At  D  a  vertical  shaft  is  sunk.     From  A  a  tunnel  is  run  in  a  north- 
easterly direction  at  right  angles  to  AB  for  160  ft.  to  a  point  Ef 
underground.     It  is  then  desired  to  run  from  E'  to  a  point  D'  at 
the  bottom  of  the  shaft  directly  under  D.     What  angle  AE'D' 
should  be  turned  off  clockwise? 

If  the  elevation  of  A  is  260.18  ft.  and  of  D  428.16  ft.  how  deep 
will  the  shaft  be  from  D  to  D'  if  the  tunnel  from  A  to  E'  is  on  a 
5%  grade  and  from  Ef  to  Df  on  a  6%  grade? 

218.  A  traverse  is  run  on  the  surface  of  the  ground  from  a 
point  A  to  a  point  E  as  follows:  AB  =  241.2  ft.;  ABC=  129° 50'; 
£C=204.3  ft.;  5CD=238°  46',  CD=334.3ft.;  CDE=125°  18', 
DE  =  380.2  ft.     The  bearing  of  DE  =  S.  54°  28'  E.     At  E  there 
is  a  vertical  shaft  at  the  bottom  of  which  is  E'  directly  under  E. 

An  underground  traverse  is  run  from  E'  to  a  point  H '  as  fol- 
lows: A  line  M'E'  is  established  directly  below  DE.  M'E'F'  = 
DEfFf  =  103°  12',  E'F'  =  396.3  ft.;  E'F'G'  =  118°  45',  F'G'  = 
431.1  ft.;  F'G'H'=  151°  13',  G'H'= 346.3  ft.  All  angles  measured 
clockwise.  It  is  desired  to  sink  a  vertical  shaft  from  a  point  H 
on  the  surface  directly  over  H'.  H  is  to  be  located  by  two  inter- 
secting lines  passing  through  A  and  B  respectively,  and  checked 
by  a  third  line  passing  through  C.  Required  the  angles  BAH, 
ABH  and  BCH  and  the  lengths  AH,  BH  and  CH. 

219.  A  boundary  line  of  a  mining  claim  is  AB  =  S.  13°  30'  W., 
length  =  350.8  ft.      A  traverse  is  run  on  the  surface  from  A  to  D 
as  follows:    (angles  measured  clockwise)  ABC  =  91°  30',  BC  = 
226.4  ft.;  BCD  =  146°  05',  CD  =  290.2  ft.     At  D  is  a  vertical 
shaft,  D'  at  the  bottom  being  directly  under  D.     An  underground 
traverse   is  run   from   D'  to  G'  as  follows:    CD'E'  =  135°   10', 
D'E'  =292.3  ft.;  D' E'F' =  87°  20',  E'F' =  192.1  ft.;  E'F'G' = 
110°  6',  F'G'  =  238.8'.     From  G'  it  is  desired  to  run  due  east  to  a 
point  H'  directly  under  the  boundary  line  AB.     Required  the 
distance  G'H'  and  the  distance  AH,  H  being  directly  over  H'. 


136  OMITTED    MEASUREMENTS. 

Questions  on  the  calculation  of  omitted  measurements.  1.  Why 
is  the  check  given  at  the  top  of  p.  400  better  than  the  one  on 
the  preceding  page?  2.  How  may  triangulation  be  checked? 
(Remark  448  (c),  p.  400.)  3.  Can  triangulation  nets  be  solved 
by  right-angled  triangle  methods?  4.  Explain  by  a  sketch  the 
trigonometric  relations  between  bearing,  length,  latitude,  and 
departure.  5.  What  are  "missing  parts  "  in  a  polygon  and 
how  many  parts  may  be  omitted  and  still  have  the  polygon 
determinate?  6.  What  are  the  four  general  cases  in  calcula- 
tion of  omitted  measurements?  p  401.  7.  What  is  the  principal 
difference  between  Case  I  and  the  other  three  cases?  8.  Explain 
the  method  of  Case  I.  9.  Explain  the  general  method  of  Cases 
II,  III,  and  IV.  10.  In  Cases  II,  III,  and  IV,  show  by  figure 
that  it  is  immaterial  whether  the  two  sides  affected  by  omitted 
measurements  are  adjacent  or  not,  p.  402,  §  451  (d).  11.  Why 
are  two  answers  possible  in  Cases  II  and  III?  12.  Explain  a 
second  method  used  for  Case  II  and  Case  III.  13.  When  is 
Case  IV  indeterminate?  14.  Answer  the  question  at  the  end 
of  the  chapter,  p.  406. 


GROUP  A. 

AREAS. 


Exercise  A-l. 
The  Use  of  the  Planimeter. 

Reference:  Page  408,  §  457. 

Directions:  Study  carefully  the  directions  of  §  457  (c)  and  the 
practical  suggestions  on  p.  409.  This  exercise  is  intended  merely 
to  teach  the  use  of  the  planimeter.  Additional  practice  in  the 
use  of  the  instrument  should  be  obtained  by  checking  the  areas 
found  in  some  of  the  other  exercises  by  computations. 

Problem:  Draw  accurately  a  circle  of  4"  diameter,  a  square 
3"  on  a  side,  and  a  hexagon  inscribed  in  a  circle  5"  in  diameter. 
Using  the  planimeter  find  the  area  of  each  of  these  three  figures 
and  check  the  results  by  computations. 

Questions:  1.  Give  the  general  method  of  using  the  planim- 
eter. 2.  Does  it  make  any  difference  whether  the  fixed  point 
is  placed  within  or  without  the  boundary?  3.  Give  some 
practical  suggestions,  p.  409.  4.  What  tests  should  be  made 
before  using  the  planimeter?  General  direction,  p.  410. 

Exercise  A-2. 

To  Compute  Areas  Directly  from  Field  Measure- 
ments. 

Reference:  Page  410. 

Directions:  Compute  the  area  of  a  polygon  directly  from 
measurements  by  the  methods  explained  in  §  458,  giving  the 
answer  in  square  feet  and  in  acres.  Before  beginning  this 
exercise,  make  out  a  table  in  which  43560  is  multiplied  by  each 
digit  from  2  to  9.  (See  p.  377.)  Do  not  carry  computations 
farther  than  the  data  will  warrant.  (See  p.  369,  §  425.) 

Problem:  (To  be  assigned  from  the  six  problems  given 

below.) 

137 


138 


AREAS. 


PROBLEMS. 


231.  The  lengths  of  the  sides  of  a  four-sided  polygon  are  as 
follows:  AB  =  91.0  ft.,  BC  =  83.9  ft.,  CD  =  113.9  ft.,  DA  = 
91.1  ft.     The  diagonal  AC  =  130.2  ft.     Find  the  area  of  the 
polygon. 

232.  The  lengths  of  the  sides  of  a  four-sided  polygon  are  as 
follows:     AB  =  75.3  ft.,  BC  =  129.6  ft.,  CD  =  97.0  ft.,  DA  = 
98.3  ft.     The  diagonal  AC  =  132.4  ft.     Find  the  area  of  the 
polygon. 

233.  The  lengths  of  the  sides  of  a  four-sided  polygon  are  as 
follows:  AB  =  120.4  ft.,  BC  =  83.6  ft.,  CD  =  76.4  ft.,  DA  = 
94.7  ft.     From  a  point  E  near  the  center  of  the  polygon  dis- 
tances are  as  follows:  EA  =  75.0  ft.,  EB  =  71.2  ft.,  EC  =  54.7 
ft.,  ED  =  62.7  ft.     Find  the  area  of  the  polygon. 

234.  The  lengths  of  the  sides  of  a  four-sided  polygon  are  as 
follows:  AB  =  85.5  ft.,  BC  =  98.0  ft.,  CD  =  101.0  ft.,  DA  = 
99.0  ft.      From  a  point  E  near  the  center  of  the  polygon  dis- 
tances  are   as   follows:  EA  =  54.9   ft.,    EB  =  63.3   ft.,    EC  = 
69.0  ft.,  ED  =  83.2  ft.     Find  the  area  of  the  polygon. 

235.  Find  the  area  of  the  polygon  in  Fig.  178,  p.  120.     See 
also  p.  410,  §  458  (c). 

236.  Find  the  area  of  the  polygon  A  BCD,  p.  179.     See  also 
p.  410,  §  458  (c). 


Exercise  A-3. 
Calculation  of  Areas  from  Offsets. 

Reference:  Pages  411  to  413. 

Directions:  Where  offsets  are  at  regular  intervals  use  the 
"Trapezoidal  Rule,"  p.  411.  Where  offsets  are  at  irregular 
intervals  use  the  first  method,  p.  412,  §  459  (c),  and  check  by 
the  second  method,  arranging  the  work  in  determinate  array  as 
indicated  in  the  illustration  on  p.  413. 

Problem:  (To  be  assigned  from  the  four  problems  given 

below.) 


AREAS.  139 

PROBLEMS. 

241.  Offsets  at  25-ft.  intervals  are  as  follows:  0+0  =  20  ft., 
0+  25=14  ft.,  0  +  50  =  18  ft.,  0  +  75  =  6  ft.,  1  +  0  =  12  ft., 
1+  25=  16  ft.,  1  +  50  =  21  ft.,  1+  75  =  18  ft.,  2  +  0  =  14  ft. 
Find  the  area  in  square  feet. 

242.  Offsets  at  50-ft.  intervals  are  as  follows:  0  +  0  =  18  ft., 
0  +  50  =  23  ft.,   1+  0  =  36  ft.,  1  +  50  =  30  ft.,  2  +  0  =  16  ft., 
2  +  50  =  28  ft.,  3  +  0  =  37  ft.,  3  +  50  =  41  ft.,  4  +  0  =  21  ft. 
Find  the  area  in  square  feet. 

243.  Offsets  at  irregular  intervals  are  as  follows:  0  +  0  =  12  ft., 

0  +  20  =  18  ft.,  0  +  60  =  24  ft.,  0  +  82  =  15  ft.,  0  +  95  =23  ft., 

1  +  10  =  43  ft.,  1  +  28  =  31  ft.,  1  +  50  =  38  ft.,  1  +  90  =  17  ft., 

2  +  20  =  28  ft.,  2  +  40  =  20  ft.     Find  the  area  in  square  feet. 

244.  Offsets  at  irregular  intervals  are  as  follows:  0  +  0  =  46  ft., 

0  +  30  =  31  ft.,  0  +  50  =  38  ft.,  0  +  80  =  24  ft.,  0  +  96=  12  ft., 

1  +  16  =  27  ft.,  1  +  30  =  22  ft.,  1  +  70  =  14  ft.,  2+10=  28  ft., 

2  +  40  =  36  ft.,  2  +  70  =  25  ft.,  3  +  20  =  8  ft.    Find  the  area 
in  square  feet. 

Exercise  A-4. 

Calculation  of  Areas  from  Latitudes  and  Double 
Longitudes. 

Reference:  Page  413. 

Directions:  Follow  the  method  of  procedure  on  p.  416,  arrang- 
ing the  work  as  shown  at  the  bottom  of  p.  417.  It  is  well  at 
first  to  compute  the  areas  of  figures  whose  latitudes  and  depar- 
tures have  been  calculated  in  previous  problems  and  thus  avoid 
the  work  involved  in  the  first  step. 

Problem, :  (To  be  assigned  from  the  sixteen  problems 

given  below.) 

PROBLEMS. 

Note:  In  each  of  the  first  seven  problems  the  student  may  use  the  lati 
tudes  and  departures  which  he  may  have  already  calculated  in  the  corre- 
sponding problem  on  p.  122.* 

251.  Calculate  the  area  of  the  polygon  in  Problem  71,  p.  122.* 

252.  Calculate  the  area  of  the  polygon  in  Problem  72,  p.  122.* 

253.  Calculate  the  area  of  the  polygon  in  Problem  73,  p.  122,* 


140  AREAS. 

254.  Calculate  the  area  of  the  polygon  in  Problem  74,  p.  122.* 

255.  Calculate  the  area  of  the  polygon  in  Problem  75,  p.  122.* 

256.  Calculate  the  area  of  the  polygon  in  Problem  76,  p.  122.* 

257.  Calculate  the  area  of  the  polygon  in  Problem  77,  p.  122.* 

258.  From  the  latitudes  and  departures  tabulated  on  p.  394, 
calculate  the  area  of  the  figure  on  p.  392. 

259.  Calculate  the  area  of  the  polygon  in  one  of  the  problems 
(to  be  assigned)  from  79  to  85  inclusive,  pp.  122,  123.* 

260.  Calculate  the  area  of  one  of  the  triangulation  nets  in 
Exercise  T-l,  p.  125,*  by  the  method  of  latitudes  and  double 
longitudes,  and  check  the  result  by  the  use  of  Formula  12,  p.  408. 

261.  Calculate  the  area  of  the  polygon  in  Problem  127,  p.  128.* 

262.  Calculate  the  area  of  the  polygon  in  Problem  128,  p.  128.* 

263.  Calculate  the  area  of  the  polygon  in  one  of  the  problems 
of  Exercise  O-2,  p.  129.* 

264.  Calculate  the  area  of  the  polygon  in  one  of  the  problems 
of  Exercise  O-3,  p.  131.* 

265.  Making  use  of  the  results  obtained  in  Problem  212,  p.  134,* 
find  the  area  in  square  feet  of  the  polygon  1-2-3-4  on  p.  177. 

266.  Making  use  of  the  results  obtained  in  Problem  214,  p.  134,* 
calculate  the  area  of  the  land  described  on  p.   183.     Use  the 
method  of  latitudes  and  double  longitudes  except  for  the  por- 
tion between  CB  and  the  edge  of  the  brook;    this  should  be 
calculated  from  the  offsets.     (See  also  illustration  at  bottom 
of  p.  419  for  explanation  of  method.) 

Questions:  1.  What  is  usually  taken  as  a  reference  merid- 
ian? p.  414.  2.  How  is  the  most  westerly  station  determined? 
p.  472.  3.  What  is  meant  by  the  first  and  last  courses?  p.  414. 
4.  What  is  the  longitude  of  a  course  and  how  is  it  obtained 
from  the  longitude  of  the  preceding  course?  5.  Explain  by 
means  of  a  sketch  the  general  method  of  calculating  areas 
from  latitudes  and  longitudes.  6.  Why  are  double  longitudes 
used  and  how  is  a  double  longitude  of  any  course  obtained 
from  the  longitude  of  the  preceding  course?  p.  416.  7.  Outline 
the  general  method  of  computing  areas  from  latitudes  and 
double  longitudes,  p.  416.  8.  What  are  some  of  the  sources  of 
mistakes?  p.  417.  9.  By  means  of  a  sketch  explain  the  method 


ABBAS.  141 

of  computing  areas  from  coordinates,  p.  418.  10.  Explain  two 
general  methods  of  computing  irregular  areas,  p.  419.  11.  Com- 
pare the  two  methods,  p.  420. 

Exercise  A-5. 

To  Part  Off  a  Required  Area  by  a  Line  Having  a  Given 
Direction. 

Reference:  Case  I,  p.  422. 

Directions:  Follow  the  method  of  procedure  of  Case  I,  p.  422. 
Before  beginning  the  exercise  study  carefully  the  illustration  on 
p.  423. 

Problem:  .  (To  be  assigned  from  the  fourteen  problems  given 
below.) 

PROBLEMS. 

Note:  In  each  of  the  first  nine  problems  the  student  may  use  the  area 
already  calculated  in  the  corresponding  problem  on  p.  139  or  p.  140.* 

271.  Divide  the  polygon  in  Problem  253,  p.  139,*  into  two 
parts  having  equal  areas  by  a  line  parallel  to  CD. 

272.  Divide  the  polygon  in  Problem  254,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  parallel  to  DA. 

.273.   Divide  the  polygon  in  Problem  255,  p..  140,*  into  two 
parts  having  equal  areas  by  a  line  whose  bearing  is  N.  30°  W. 

274.  Divide  the  polygon  in  Problem  256,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  whose  bearing  is  N.  60°  W. 

275.  Divide   the  polygon  in  Problem  257,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  whose  bearing  is  S.  60°  E. 

276.  Divide  the  polygon  in  Problem  258,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  whose  bearing  is  N.  75°  E. 

277.  Same  as  Problem  276  except  the  bearing  of  the  divid- 
ing line  is  N.  4°  W. 

278.  Divide  the  polygon  in  Problem  261,  p.  140,*  into  two 
parts  one  of  which  (bounded  by  the  line  NO)  has  an  area  double 
that  of  the  other.     The  bearing  of  the  dividing  line  is  N.  45°  W. 

279.  Divide  the  polygon  in  Problem  262,  p.  140,*  into  two 
parts  one  of  which  (bounded  by  the  line  M N)  has  an  area  double 
that  of  the  other.     The  dividing  line  is  parallel  to  MN. 


142  AREAS. 

280.  Find  the  position  of  a  line  parallel  to  AB  which  will 
divide  the  polygon  ABCDEF  into  two  equal  parts.     The  lati- 
tudes and  departures  of  the  lines  are  as  follows:   AB  =  400  ft.  S., 
800  ft.  E.;   BC  =  300  ft.  S.,  500  ft.  W.;   CD  =  600  ft.  S.,  400 
ft.  E.;    DE  =  200  ft.  S.,  1000  ft.  W.;    EF  =  900  ft.  N.,  600 
ft.  W.;  FA  =  600  ft.  N.,  900  ft.  E. 

281.  Find  the  position  of  a  line  parallel  to   ED  which  will 
divide  the  polygon  ABODE  into  two  equal  parts.     The  lati- 
tudes and  departures  of  the  lines  are  as  follows:    EA  =  1500 
ft.  N.,  300  ft.  E.;  AB  =  400  ft.  S.,  800  ft.  E.;   BC  =  300  ft.  S., 
500  ft.  W. ;  CD  =  600  ft.  S.,  400  ft.  E. ;  DE  =  200  ft.  S.,  1000  W. 

282.  Same  as  Problem  280  except  that  the  area  to  be  parted 
off  is  10  acres,  bounded  on  one  side  by  AB. 

283.  Same  as  Problem  281  except  that  the  area  to  be  parted 
off  is  8  acres,  bounded  on  one  side  by  ED. 

284.  Divide  the  land  described  on  p.  179  into  two  equal  parts 
by  a  line  perpendicular  to  the  street  line. 

Exercise  A-6. 

To  Part  Off  a  Required  Area  by  a  Line  Starting  from 
a  Given  Point. 

Reference:  Case  II,  p.  424. 

Directions:  Follow  the  method  of  procedure  of  Case  II, 
p.  424.  Before  beginning  the  exercise  study  carefully  the  illus- 
tration on  p.  426. 

Problem:  .  (To  be  assigned  from  the  fourteen  problems 
given  below.) 

PROBLEMS. 

Note:  In  each  of  the  first  nine  problems  the  student  may  use  the  area 
already  calculated  in  the  corresponding  problem  on  p.  139*  or  p.  140.* 

291.  Divide  the  polygon  in  Problem  253,  p.  139,*  into  two 
parts  having  equal  areas  by  a  line  starting  from  the  point  A. 

292.  Divide  the  polygon  in  Problem  254,  p.  140,*  into  two  parts 
having  equal  areas  by  a  line  starting  from  the  point  B. 

293.  Divide  the  polygon  in  Problem  255,  p.  140,*  into  two  parts 
having  equal  areas  by  a  line  starting  from  a  point  half  way 
between  A  and  E. 


AREAS.  143 

294.  Divide  the  polygon  in  Problem  256,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  starting  from  a  point  half 
way  between  B  and  C. 

295.  Divide  the  polygon  in  Problem  257,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  starting  from  a  point  half 
way  between  5  and  1. 

296.  Divide  the  polygon  in  Problem  258,  p.  140,*  into  two 
parts  having  equal  areas  by  a  line  starting  from  the  point  Q. 

297.  Same  as  Problem  296  except  the  dividing  line  starts  from 
the  point  V  instead  of  Q. 

298.  Divide  the  polygon  in  Problem  261,  p.   140,*  into  two 
parts  one  of  which  (bounded  by  the  line  NO)  has  an  area  double 
that  of  the  other.     The  dividing  line  starts  from  M. 

299.  Divide  the  polygon  in  Problem  262,  p.  140,*  into  two 
parts  one  of  which  (bounded  by  the  line  MN)  has  an  area  double 
that  of  the  other.     The  dividing  line  starts  from  Q. 

300.  Same  as  Problem  280  of  the  preceding  exercise,  p.  142,* 
except  that  the  dividing  line  starts  from  A,  its  direction  being 
unknown. 

301.  Same  as  Problem  281  of  the  preceding  exercise,  p.  142,* 
except  that  the  dividing  line  starts  from  C,  its  direction  being 
unknown. 

302.  Same  as  Problem  282  of  the  preceding  exercise,  p.  142,* 
except  that  the  dividing  line  starts  from  C,  its  direction  being 
unknown. 

303.  Same  as  Problem  283  of  the  preceding  exercise,  p.  142,* 
except  that  the  dividing  line  starts  from  a  point  on  EA  500  ft. 
from  E. 

304.  Divide  the  land  described  on  p.  179  into  two  equal  parts 
by  a  line  starting  from  the  middle  of  the  western  side. 


GROUP  E. 

EARTHWORK   CALCULATION. 


Exercise  E-l. 

To  Calculate  Earthwork  by  the  Method  of  Unit 
Areas. 

(All  cut  or  all  fill.) 

References:  Pages  428  to  430,  also  page  287,  §  362. 

Directions:  Before  beginning  the  computation  make  a  sketch 
as  directed  in  the  method  of  procedure  at  the  bottom  of  p.  430. 
Follow  this  method  of  procedure  closely,  observing  the  practical 
suggestion  on  p.  431. 

Problem:  (To  be  assigned  from  the  fourteen  problems 

given  below.) 

PROBLEMS. 

When  the  finished  surface  is  level. 

311.  A  rectangular  plot  is  divided  into  20-ft.  squares  and  the 
corners  are  numbered  according  to  the  system  shown  in  Fig. 
402  (c),  p.  341.  The  elevations  at  each  corner  in  feet  are  as 
follows: 


AQ 
Al 
A2 
A3 

A4: 

AS 
AQ 
BO 
Bl 

=  28.1, 
=  26.2, 
=  24.3, 
=  27.1, 
=  22.4, 
=  21.9, 
-  26.3, 
=  25.2, 
=  23.2, 

B2 
B3 
54 
B5 
BQ 
CO 
Cl 
C2 
C3 

=  25.9, 
=  22.2, 
=  20.1, 
=  19.4, 
=  24.3, 
=  23.1, 
=  20.1, 
=  21.8, 
=  19.4, 

C4 
C5 
C6 
Z>0 
Dl 
D2 
D3 
D4 
D5 

- 

17.6, 
16.1, 
18.4, 
20.2, 
17.4, 
16.9, 
15.4, 
14.5, 
13.2, 

DQ 
EQ 
El 
E2 
E3 
E4 
E5 
EG 
FO 

= 

15.4, 
23.8, 
21.2, 
18.0, 
17.8, 
18.9, 
21.1, 
22.3, 
24.0, 

Fl 
F2 
F3 

F4: 

F5 
FQ 

=  25.1, 
=  26.4, 
=  26.9, 
=  25.3, 
=  23.8, 
=  27.1. 

If  the  ground  is  graded  to  a  level  surface  whose  elevation  is 
12  ft.,  find  the  amount  of  earth  to  be  removed.  Answer  in 
cubic  yards. 

144 


EARTHWORK   CALCULATION.  145 

312.  Same  as  Problem  311  except  it  is  required  to  find  the 
amount  of  earth  which  must  be  filled  in  to  bring  the  entire  lot  to 
a  level  surface  whose  elevation  is  30  ft. 

313.  Same  as   Problem  311  except  that   the  unit  area  is  a 
50-ft.  square  and  the  elevation  of  the  level  surface  is  8.4  ft. 

314.  Same  as  Problem  312  except  that  the  unit  area  is  a 
50-ft.  square  and  the  elevation  of  the  level  surface  is  28.1  ft. 

315.  Same  as  Problem  311  except  the  unit  area  is  a  50-ft. 
square  and  the  elevation  of  the  level  surface  is  9.9  ft. 

316.  Same  as  Problem  312  except  the  unit  area  is  a  50-ft. 
square  and  the  elevation  of  the  level  surface  is  29.2  ft. 

When  the  finished  surface  slopes  in  one  direction  only. 

317.  Assume  the  data  given  in  Problem  311.     The  elevation  of 
the  finished  surface  at  AQ  and  FQ  is  12  ft.,  and  this  surface  slopes 
downward  at  the  rate  of  1  ft.  per  100  ft.  to  the  line  between  AQ 
and  FQ  which  is  horizontal.     Find  the  amount  of  earth  to  be 
removed. 

318.  Assume  the  data  given  in  Problem  311.     The  elevation  of 
the  finished  surface  at  AQ  and  FQ  is  30  ft.,  and  this  surface 
slopes  upward  at  the  rate  of  0.5  ft.  per  100  ft.  to  the  line  between 
AQ  and  FQ  which  is  horizontal.     Find  the  amount  of  earth  to 
t>e  added. 

319.  Same  as  Problem  317  except  the  slope  is  1.5  ft.  per  100  ft. 

320.  Same  as  Problem  318  except  the  slope  is  1.0  ft.  per  100  ft. 

When  the  finished  surface  slopes  in  two  directions. 

321.  Assume  the  data  given  in  Problem  311.     The  plane  of  the 
finished  surface  is  determined  by  two  lines,  one  from  .40  to  -46, 
the  other  from  AQ  to  FQ.     The  elevation  of  this  surface  at  AQ  is 
13  ft. ;  at  46,  11.5  ft. ;  at  FQ,  12.5  ft.     Find  the  amount  of  earth 
to  be  removed. 

322.  Same  as  Problem  321  except  the  elevation  of  the  finished 
surface  at  AQ  is  30  ft. ;  at  AQ,  31.2  ft. ;  at  FQ,  29.0  ft.     Find  the 
amount  of  earth  to  be  added. 

323.  Same  as  Problem  321  except  the  unit  area  is  a  50-ft.  square 
and  the  elevation  of  the  finished  surface  at  AQ  is  10  ft.;  at  AQ, 
11. 8  ft.;  and  at  FQ,  12.3  ft. 


146  EARTHWORK   CALCULATION. 

324.  Same  as  Problem  322  except  the  unit  area  is  a  50-ft.  square 
and  the  elevation  of  the  finished  surface  at  AO  is  28.1  ft.;  at  A6, 
29.9  ft.;  and  at  FQ,  30.9  ft. 

Questions:  1.  What  is  meant  by  a  3  per  cent  grade  or  gradient? 
p.  428.  2.  How  are  the  elevations  at  different  points  corre- 
sponding to  a  given  grade  calculated?  p.  428.  3.  What  is  the 
cut  or  fill  at  any  point,  and  the  corresponding  algebraic  signs? 
p.  429.  4.  What  is  a  polyhedron;  a  truncated  prism;  a  right- 
truncated  prism?  p.  429.  5.  What  is  the  volume  of  a  truncated 
prism  equal  to?  6.  Give  the  general  method  of  calculating 
earthwork  from  unit  areas,  p.  429.  7.  Explain  the  method  of 
procedure  when  the  finished  surface  slopes  in  one  direction; 
when  it  slopes  in  two  directions.  8.  Explain  the  method  of 
procedure  when  the  outline  of  an  area  is  not  rectangular,  p.  431. 

9.  Give    suggestions:  (a)    For   a    systematic    method    of    com- 
putation, p.  431 ;  (b)  as  regards  the  size  of  a  unit  square,  p.  432. 

10.  In  very  uneven  ground  how  may  the  method  of  unit  rec- 
tangles or  squares  be  modified  to  obtain  greater  accuracy?  p.  432. 


Exercise  E-2. 

To  Calculate  Earthwork  by  the  Method  of  Unit 
Areas. 

(Irregular  Boundaries.) 

This  exercise  is  the  same  as  the  preceding  exercise  except  that 
the  outline  of  the  area  to  be  graded  is  not  rectangular,  but 
irregular.  The  instructor  should  make  up  a  problem  similar  to 
that  indicated  in  Fig.  467  (g),  p.  431,  or  Fig.  468,  p.  432,  estab- 
lishing the  elevations  for  the  finished  surface  in  such  a  way  that 
it  will  lie  entirely  below  or  above  the  original  surface,  i.e.,  so 
that  the  grading  will  be  all  cut  or  all  fill. 


EARTHWORK   CALCULATION.  147 


Exercise  E-3. 

To  Estimate  Cut  and  Fill  by  the  Method  of 
Unit  Areas. 

Reference:  Page  432,  §  468. 

Directions:  Before  beginning  the  computation,  make  a  sketch 
as  directed  in  the  method  of  procedure  at  the  bottom  of  p.  430. 
Determine  by  interpolation  the  points  where  there  is  neither  cut 
nor  fill.  (See  p.  433.)  Calculate  separately  the  cut  and  the 
fill,  each  by  the  method  of  §  467  (e),  p.  430.  For  the  methods 
of  interpolation  see  §  469,  p.  433;  also  p.  497. 

Problem:  (To  be  assigned  from  the  thirteen  problems 

given  below.) 


PROBLEMS. 

When  the  finished  surface  is  level. 

331.  A  rectangular  plot  is  divided  into  20-ft.  squares  and  the 
corners  are  numbered  according  to  the  system  shown  in  Fig.  402 
(c),  p.  341.     The  elevations  at  each  corner  in  feet  are  as  follows: 

AQ  =  42.4,  53  =  41.6,  C6  =  36.0,  E2  =  38.7,  F5  =  33.2, 

Al  =  41.3,  £4  =  39.9,  DO  =  41.6,  E3  =  36.3,  ,P6  =  31.7, 

A2  =  42.1,  B5  =  39.2,  Dl  =  40.9,  E4  =  37.2,  GO  =  45.8, 

A3  =  43.2,  56  =  37.1,  1)2  =  41.0,  #5  =  36.1,  Gl  =  43.4, 

44  =  39.6,  CO  =  44.2,  D3  =  41.4,  EG  =  35.0,  G2  =  41.2, 

A5  =  38.7,  Cl  =  45.6,  Z>4  =  40.3,  FO  =  43.2,  G3  =  39.7, 

AQ  =  36.3,  C2  =  43.9,  D5  =  39.1,  Fl  =  42.1,  G4  =  37.4, 

BO  =  43.1,  C3  =  42.1,  Z>6  =  36.9,  F2  =  37.8,  G5  =  31.0, 

Bl  =  44.0,  C4  =  41.8,  EQ  =  42.6,  F3  =  35.4,  GQ  =  30.0. 

B2  =  42.8,  C5  =  39.9,  El  =  41.4,  F4  =  34.6, 

Calculate  the  cut  and  fill  required  to  grade  the  plot  to  a  level 
surface  whose  elevation  is  40.0  ft.     Answer  in  cubic  yards. 

332.  Same  as  Problem  331  except  the  elevation  of  the  level 
surface  is  39.0  ft. 

333.  Same  as  Problem  331  except  that  the  unit  area  is  a  50-ft. 
square  and  the  elevation  of  the  level  surface  is  37.0  ft; 


148  EARTHWORK   CALCULATION. 

334.  Same  as  Problem  331  except  that  the  unit  area  is  a  50-ft. 
square  and  the  elevation  of  the  level  surface  is  42.0  ft. 

335.  What  should  be  the  elevation  of  the  level  surface  in  Prob- 
lem 331  in  order  to  make  cut  and  fill  equal? 

When  the  finished  surface  slopes  in  one  direction  only. 

336.  Assume  the  data  given  in  Problem  331.    The  elevation  of 
the  finished  surface  at  AO  is  40.0  ft. ;  atA6,  38.5  ft. ;  at  GO,  40.0  ft. ; 
and  at  G6,  38.5  ft.     Calculate  the  cut  and  fill  in  grading  to  a 
plane  surface  determined  by  these  four  elevations. 

337.  Same  as  Problem  336  except  the  elevations  are  as  follows: 
AO,  41.0  ft.;  A6,  38.0  ft.;  GO,  41.0  ft.;  GQ,  38.0  ft. 

338.  Same  as  Problem  336  except  the  unit  area  is  a  50-ft.  square 
and  the  elevations  are  as  follows:     AQ,  39.0  ft.;  AQ,  37.5  ft.; 
GO,  39.0  ft. ;  G6,  37.5  ft. 

339.  Same  as  Problem  336  except  the  unit  area  is  a  50-ft.  square 
and  the  elevations  are  as  follows:   AO,   41.0  ft.;  AQ,   39.2   ft.; 
GO,  41.0ft.;G6,  39.2ft. 

When  the  finished  surface  slopes  in  two  directions. 

340.  Assume  the  data  given  in  Problem  331.     The  plane  of  the 
finished  surface  is  determined  by  two  lines,  one  from  AQ  to  AQ, 
the  other  from  AQ  to  G6.     The  elevation  of  this  surface  at  AQ  is 
42.0  ft'. ;  at  AQ,  40.2  ft. ;  at  G6,  38.4  ft.    Calculate  the  cut  and  fill. 

341.  Same  as  Problem  340  except  the  elevation  of  the  finished 
surface  at  AQ  is  41.8  ft.;  at  AQ,  38.2  ft.;  at  G6,  39.4  ft. 

342.  Same  as  Problem  340  except  the  unit  area  is  a  50-ft.  square 
and  the  elevation  of  the  finished  surface  at  AO  is  40.2  ft.;  at 
A6,  39  .Oft.;  at  G6,  37.2ft. 

343.  Same  as  Problem   340  except  the  unit  area  is  a  50-ft. 
square  and  the  elevation  of  the  finished  surface  at  AO  is  39.0  ft.; 
at  A6,  40.2  ft. ;  at  G6,  38.4  ft. 

Exercise  E-4. 

To  Calculate  Cut  and  Fill  by  the  Method  of 
Unit  Areas. 

(Irregular  Boundaries.) 

This  exercise  is  the  same  as  Exercise  E-2,  p.  146,*  except  that 
the  finished  surface  is  such  that  the  calculations  will  be  for  both 
cut  and  fill,  instead  of  for  all  cut,  or  for  all  fill. 


EARTHWORK    CALCULATION.  149 


Exercise  E-5. 

Calculation  of  Earthwork  for  Ditches  and  Em- 
bankments. 

Reference:  Page  434,  §  470. 

Directions:  Find  the  area  of  each  cross-section  in  succession, 
either  by  the  use  of  the  planimeter  or  by  calculation,  and  apply 
the  "end  area"  formula  to  the  solids  between  the  respective 
cross-sections  as  explained  in  §  470. 

Note:  If  desired,  the  problems  may  also  be  solved  by  the  "prismoidal 
formula."  The  problems  are  made  simple  tmrposely,  it  being  taken  for 
granted  that,  in  most  cases,  the  student  will  study  this  part  of  the  subject 
to  better  advantage  in  connection  with  railway  surveying. 


PROBLEMS. 

351.  A  ditch  is  8.0  ft.  wide  at  the  bottom,  and  falls  0.5  ft. 
in  100  ft.;  its  sides  slope  outward  1£  horizontal  to  1  vertical. 
The  elevation  at  the  bottom  of  the  ditch  at  0  +  0  =  20.0  ft. 
The  elevations  of  the  three  points  on  the  surface  of  the  ground  at 
each  station  are  as  follows:  at  0  +0,  C  (the  center  height)  = 
32.1  ft.,  R  (the  right-hand  edge  of  the  ditch)  =  31.1  ft.,  L  (the 
left-hand  edge  of  the  ditch)  =  33.6  ft.;  at  0  +  50,  C  =  31.6  ft., 
R  =  30.8  ft.,  L  =  32.4  ft.;  at  1+  00,  C  =  30.1  ft.,  R  =  28.7  ft., 
L  =  31.0  ft.;  at  1  +  60,  C  =  28.2  ft.,  R  =  26.4  ft.,  L  =  29.1  ft.; 
at  2+  00,  C  =  24.3  ft.,  R  =  23.1  ft.,  L  =  25.3  ft.     Calculate 
the  earth  to  be  removed  from  the  portion  of  the  ditch  given 
above. 

352.  Same  as  Problem  351  except  the  bottom  of  the  ditch  is 
10.0  ft.  wide  and  the  sides  slope  outward  l£  horizontal  to  1 
vertical. 

353.  Assume  the  elevations  on  the  surface  of  the  ground  to  be 
the  same  as  in  Problem  351.     It  is  desired  to  build  an  embank- 
ment, the  top  of  which  is  8.0  ft.  wide  and  at  an  elevation  of 
36.0  ft.     The  sides  slope  1$  horizontal  to  1  vertical.     Calculate 
the  total  fill. 

354.  Same  as  Problem  353  except  the  top  of  the  embankment 
is  10.0  ft.  wide  and  at  an  elevation  of  38.0  ft.     The  sides  slope 
l    horizontal  to  1  vertical. 


150  EARTHWORK    CALCULATION. 

Questions:  1.  Define  prismoid.  2.  A  transverse  slope  is  de- 
noted by  the  horizontal  distance  which  corresponds  to  a  vertical 
distance  of  one  unit.  How  does  this  differ  from  the  method 
ordinarily  used  in  denoting  a  longitudinal  slope  (commonly  called 
"grade")?  3.  Give  the  "end  area"  formula.  4.  Give  the 
"prismoidal"  formula.  5.  Which  gives  the  better  results? 
6.  In  the  "prismoidal "  formula  is  the  area  M  the  mean  of  the 
two  end  areas;  how  is  it  obtained?  7.  What  is  meant  by  "  three- 
level  "  cross-sections?  8.  For  "three-level"  sections  how  may 
the  work  of  computation  be  shortened? 


Exercise  E-6. 
To  Estimate  Cut  and  Fill  from  a  Contour  Map. 

Reference:  Page  435. 

Directions:  The  problem  in  this  exercise  is  to  estimate  the  cut 
and  fill  from  a  contour  map,  using  one  or  more  methods  explained 
in  §  471,  p.  435.  A  contour  map  already  plotted  may  be  used, 
or  a  fictitious  map  similar  to  that  shown  in  Fig.  471  (a),  p.  435, 
may  be  drawn  and  used  as  a  basis  for  computation. 

Questions:  1.  Explain  in  detail  the  first  method,  p.  435. 
2.  Explain  the  second  method,  p.  436.  3.  Explain  the  third 
method,  p.  436,  illustrating  it  by  means  of  a  sketch. 


GROUP  P. 

EXERCISES  IN  PLOTTING. 


Exercise  P-l. 
Use  of  Drawing  Instruments. 

References:  Pages  438  to  442  and  pages  445  to  449. 

Preparations  of  instruments:  I.  First  of  all,  sharpen  the  pencil 
properly  and  then  keep  it  sharp.  See  remark,  p.  438.  Every 
student  is  required  to  keep  at  hand  a  piece  of  sandpaper  and  a 
cloth  which  may  be  suspended  from  the  corner  of  the  drawing 
table  for  convenience.  2.  Insert  a  hard  lead  in  the  compasses 
and  sharpen  it  to  a  cone  shape  point.  See  p.  442,  §  478  (1). 
3.  Adjust  the  pivot  needle,  p.  442,  §  478  (2).  4.  Make  a 
pricking  point  by  inserting  a  needle  in  a  wooden  or  a  wax  handle. 
See  p.  418,  §  486.  5.  Test  the  edge  of  the  T-square  for  straight- 
ness.  See  footnote,  p.  438.  6.  Test  the  right  hand  edge  of  the 
drawing  board  for  straightness  by  bringing  the  upper  edge  of  the 
T-square  into  contact  with  it.  In  a  similar  manner  see  if  the  sur- 
face of  the  board  is  a  plane.  7.  Test  the  triangles  as  directed  in 
the  footnote,  p.  439.  8.  Either  during  this  exercise  or  previous 
to  the  next  exercise,  the  student  should  prepare  a  protractor 
similar  to  that  described  on  p.  456,  §  493  (c). 

Note:  While  the  student  is  supposed  to  have  had  a  course  in  mechanical 
drawing  before  beginning  this  course,  nevertheless,  it  will  be  found  advan- 
tageous to  devote  the  first  exercise  in  plotting  to  a  drill  in  those  methods 
of  drafting  which  are  of  especial  importance  in  mapping.  The  exercise 
will  be  of  little  value,  however,  unless  the  student  is  careful  to  observe  the 
precautions  outlined  above,  precautions  which,  if  taken  throughout  the 
course,  will  enable  him  to  secure  more  accurate  results  than  he  otherwise 
could.  Additional  suggestions  for  drafting  should  be  reviewed  in  a  recita- 
tion on  the  questions  given  at  the  end  of  this  exercise. 


PROBLEMS. 

361.  (1)  Draw  a  horizontal  line  about  10"  long.  (Read  §  483, 
p.  446.)  (2)  Set  the  zero  mark  of  the  scale  at  an  assumed  point 
A  on  the  horizontal  line,  and  without  moving  the  scale  lay  off  in 
succession  to  a  scale  of  1"  =  20'  —  0"  the  following  distances : 

151 


152  EXERCISES  IN  PLOTTING. 

AB  =  30  ft.,  BCf=42  ft.,  OD  =  65.5  ft.,  and  DE=21.5  ft.  Check: 
AE  =  159.0  ft.  (Read  §  475,  p.  440,  and  §  486,  p.  448.)  (3) 
Draw  a  second  horizontal  line  about  10"  long,  and  in  a  similar 
manner  lay  off  (to  a  scale  of  1"  =  40'-0"):  0  +  40,  0  +  60, 
1  +  10, 1  +  75,  2  +  38,  3  +  17.  (Read  §  486  (a),  p.  449.) 

Note:  In  inspecting  the  above  work  the  instructor  will  note:  (1)  If  the 
pencil  is  sharpened  correctly.  (2)  If  fine,  almost  invisible  prick-marks 
and  freehand  circles  have  been  used.  (3)  If  lengths  are  correct. 

362.  (1)  Draw  a  line  about  6"  long  at  45°  to  the  horizontal, 
and  mark  two  points  on  it  A  and  B,  128.2  ft.  apart  to  a  scale  of 
1"  =  30'  —  0".     (2)  By  means  of  the  compasses  and  scale,  estab- 
lish a  point  C  98.5  ft.  from  A  and  120.6  ft.  from  B.     Draw  only 
one  arc.     (Read  §  478,  p,  442.) 

Note:  In  inspecting  the  above  work  the  instructor  will  note  if  the  com- 
passes were  used  correctly,  and  if  the  three  lengths  are  correct.  If  a  visible 
hole  was  left  in  the  paper  by  the  pivot  needle  of  the  compasses,  it  is  evident 
that  either  the  legs  were  not  bent,  or  too  much  pressure  was  exerted. 

363.  (1)  Draw  a  line  at  random  about  10"  long  and  inclined 
about  10°  to  the  horizontal.     (2)  Mark  off  on  this  line  421  ft.  to 
a  scale  of   1"  =  50'  — 0".     (3)  At  one  end  of  this  length  erect  a 
perpendicular  about  10"  long  by  using  two  triangles.     (Read  §  474 
(1),  p.  439.)     (4)  Lay  off  328  ft.  on  this  perpendicular.     (5)  Com- 
plete the  421  X  328  ft.  rectangle  without  further  measurement 
by  drawing  parallel  lines  with  the  two  triangles.     (Read  §  474 
(3),  p.  439.)     (6)  Check  the  rectangle  by  measuring  the  lengths 
of  the  two  diagonals. 

Note:  In  inspecting  the  above  work  the  instructor  will  note:  (1)  If 
light  hair-lines  have  been  used,  and  if  the  lines  intersect  sharply  at  cor- 
ners, running  beyond  instead  of  stopping  short.  (2)  If  right  methods  of 
erecting  perpendiculars  and  drawing  parallel  lines  were  employed.  (3)  If 
the  lengths  of  the  sides  of  a  rectangle  and  of  its  diagonals  are  correct. 

Questions:  1.  What  is  the  purpose  of  sharpening  one  end  of 
the  pencil  to  a  wedge  shape  edge?  p.  438.  2.  How  close  to  the 
ruling  edge  should  pencil  lines  be  drawn?  p.  438.  3.  Give 
additional  suggestions  for  penciling,  p.  446.  4.  Give  suggestions 
for  the  use  of  the  T-square,  p.  438.  5.  Why  should  not  the 
T-square  be  used  against  the  top  or  bottom  of  the  board  for  draw- 
ing vertical  lines?  p.  439.  6.  What  is  the  incorrect  way  of  erect- 
ing a  perpendicular  line  by  means  of  a  triangle?  7.  How  should 
the  triangles  be  used  for  erecting  perpendiculars;  for  drawing 
parallel  lines?  p.  439.  8.  Explain  the  use  of  the  decimal  scale, 
p.  440.  9.  Give  additional  suggestions  for  laying  off  measure- 
ments as  regards  marking  points;  use  of  dividers;  arithmetical 


EXERCISES  IN   PLOTTING.  153 

work;  estimating  fractions  of  a  foot;  setting  the  compasses  to  a 
given  radius;  detecting  large  errors;  detecting  small  errors; 
avoiding  the  use  of  the  wrong  edge  of  the  scale;  laying  off  plus 
stations,  p.  448.  10.  What  is  the  proper  use  of  the  dividers; 
the  improper  use;  use  of  proportional  dividers?  p.  441.  11.  Give 
suggestions  for  the  use  of  the  compass,  p.  442.  12.  Give  sug- 
gestions for  the  use  of  the  curve-ruler,  p.  442.  13.  Give  sugges- 
tions for  fastening  the  paper  to  the  board,  p.  445.  14.  Give 
precautions  to  insure  neatness,  p.  445.  15.  Give  suggestions 
for  erasing  as  regards  erasing  pencil  lines;  keeping  the  eraser 
clean;  erasing  ink  lines;  restoring  the  surface  of  the  paper;  use 
of  an.  erasing  shield ;  cleaning  tracings,  p.  447. 

Exercise  P-2. 
Methods  of  Plotting  Angles. 

Reference:  Chapter  XXXVIII,  p.  455. 

Directions:  The  angles  in  each  problem  of  this  exercise  should 
be  plotted  with  as  great  accuracy  as  the  method  used  in  that 
problem  will  permit.  Use  hair-lines  and  prick  the  points. 

PROBLEMS. 

371 .  Draw  a  horizontal  line  396  ft.  long  to  a  scale  of  I"  =  50'  -  0". 
By  means  of  the  protractor  lay  off  at  one  end  of  this  line  an 
angle  of  38°  20'  and  at  the  other  end  an  angle  of  51°  40'.     The 
two  lines  thus  obtained  and  the  original  line  should  form  a  right- 
angled  triangle ;  test  the  right  angle  by  means  of  the  two  instru- 
mental triangles.     (In  using  the  protractor,  minutes  of  arc  are 
estimated.) 

372.  Same  as  Problem  371  except  use  the  tangent  method 
for  plotting  angles,  p.  458. 

373.  Same  as  Problem  371  except  use  the  cosine  and  sine 
method,  p.  459. 

374.  Same  as  Problem   371  except  use  the  chord  method, 
p.  459. 

375.  Compare  the  results  by  drawing  an  arc  of  6"  radius  for  each 
of  the  angles  in  the  above  problems,  and  by  means  of  the  dividers 
see  if  the  corresponding  chords  are  of  the  same  length  in  all  four 
figures, 


154  EXERCISES   IN   PLOTTING. 

Questions:  1.  Name  five  methods  of  plotting  angles,  p.  455. 
2.  Give  suggestions  for  centering  the  protractor,  p.  455.  3.  Give 
three  methods  of  laying  off  an  angle  greater  than  180°,  p.  456. 
4.  How  closely  can  angles  be  plotted  with  an  ordinary  pro- 
tractor? p.  456.  5.  What  is  a  vernier  protractor?  p.  456. 
6.  What  is  the  advantage  of  the  form  of  protractor  shown 
on  p.  456?  7.  Give  suggestions  for  making  such  a  protractor, 
p.  457.  8.  Explain  the  tangent  method  of  plotting  angles, 
p.  458.  9.  Why  is  it  advantageous  to  use  a  10"  base?  10.  When 
an  angle  exceeds  45°  how  is  it  plotted?  11.  Explain  methods 
of  plotting  angles  a  little  greater  or  less  than  90°;  180°;  270°. 
12.  Give  practical  suggestions  as  regards  erecting  perpendicu- 
lars; laying  off  hundredths  of  an  inch;  using  a  base  larger  or 
smaller  than  10  inches ;  checking  angles  roughly ;  detecting  small 
mistakes ;  laying  off  angles  in  the  field,  p.  459.  13.  Explain  the 
cosine  and  sine  method  of  plotting  angles  and  give  the  check, 
p.  459.  14.  Explain  the  chord  method  of  plotting  angles, 
p.  459.  15.  Give  practical  suggestions  for  the  chord  method 
as  regards  use  of  beam  compasses  and  scale;  a  home-made 
device ;  use  of  5"  radius ;  use  of  8",  9",  or  12"  radius.  16.  Explain 
why,  if  the  radius  is  10"  and  fiftieths  on  the  scale  are  used,  it  is 
not  necessary  to  multiply  the  sine  of  half  the  angle  by  2. 
See  Fig.  496  (c),  p.  460.  17.  What  is  the  largest  angle  that  can 
be  laid  off  conveniently  by  the  chord  method  without  erecting  a 
perpendicular?  18.  Compare  the  different  methods  of  plotting 
angles,  p.  461.  19.  Explain  the  three-point  problem  in  plotting 
by  the  graphic  method;  by  the  algebraic  method. 


Methods  of  Plotting  Traverses. 

(Introductory.) 

Before  beginning  to  plot  surveys  from  notes  taken  in  the  field, 
it  is  well  for  the  student  to  have  a  preliminary  drill  in  the  different 
methods  of  plotting  traverses.  For  this  purpose  it  is  advisable 
to  select  a  polygon  of  four  or  five  sides  from  among  the  problems 
given  on  p.  122,*  and  to  plot  this  polygon  by  each  of  the  general 
methods  explained  in  Chapter  XXXIX,  p.  463.  He  will  thus 
obtain  a  knowledge  of  the  advantages  and  disadvantages  of  the 
different  methods  when  applied  to  the  same  polygon.  As 
pointed  out  on  p.  463,  for  each  of  the  four  methods  of  plotting 


EXERCISES   IN  PLOTTING.  155 

traverse  lines  there  are  four  methods  of  plotting  angles,  but  it 
is  not  worth  while  to  plot  the  polygon  sixteen  times  for  the  sake 
of  illustrating  each  of  these  methods  since  many  of  them  are  so 
nearly  alike.  The  methods  chosen  for  the  seven  succeeding 
exercises  have  been  selected  with  a  view  of  bringing  out  the  most 
important  points  connected  with  plotting  traverses.  In  each 
exercise  the  choice  of  scale  is  left  to  the  student  or  to  the  instruc- 
tor. If  desired,  different  scales  may  be  employed  for  the  different 
problems,  care  being  taken  that  the  scale  is  not  so  large  that  the 
polygon  will  run  off  the  paper,  or  so  small  that  the  accuracy  of 
the  work  is  impaired.  It  is  not  advisable  to  ink  the  drawings,  as 
time  can  be  spent  to  better  advantage  in  other  work. 


Exercise  P-3. 
Plotting  Traverses  with  a  Protractor. 

Reference:  Page  464,  §  502. 

Directions:  l.r  Assume  one  side  of  the  polygon  in  any  posi- 
tion on  the  paper  that  will  permit  the  rest  of  the  polygon  to  be 
plotted  without  running  off  the  paper.  2.  Plot  the  polygon, 
using  the  protractor  for  laying  off  angles,  and  the  scale  for 
laying  off  lengths.  3.  Not  only  should  the  line  from  the  last 
station  pass  through  the  first  station,  but  the  distance  from  the 
former  to  the  latter,  as  scaled  on  the  drawing,  should  be  equal 
to  that  given  in  the  notes.  The  student  should  make  this  test 
when  the  polygon  is  completed. 

Problem:    Plot  the  polygon  of  Problem        ,  p.  (To  be 

assigned  by  the  instructor  from  the  problems  on  p.  122.*) 

Questions:  1.  Why  is  it  important  to  plot  traverse  lines 
with  great  accuracy?  p.  463.  2.  How  great  an  error  in  feet 
may  be  caused  by  the  width  of  a  line?  3.  When  may  a  pro- 
tractor be  used  consistently  for  plotting  traverses?  p.  464. 
4.  Give  precautions  for  centering  protractor,  p.  464. 


156  EXERCISES    IN    PLOTTING. 

Exercise  P-4. 
Tangent  Method  of  Plotting  Traverses. 

Reference:  Page  464,  §  503  (a). 

Directions:  1.  Make  a  rough  freehand  sketch  in  the  note- 
book and  enter  on  this  sketch  the  lengths  and  the  angles  to  be 
plotted.  (Angles  are  not  necessarily  the  same  as  those  given  in 
the  notes.)  Check  this  data  before  proceeding.  2.  Make  out 
a  table  corresponding  to  that  at  the  top  of  p.  465.  3.  Plot 
each  of  the  transit  lines  in  succession  by  the  tangent  method. 
Check  each  angle  roughly  with  the  protractor  as  soon  as  plot- 
ted. 4.  Check  the  length  as  well  as  the  direction  of  the  last 
line. 

Problem:  Same  as  the  problem  in  Exercise  P-3  except  that 
the  tangent  method  is  used  for  plotting  angles. 

Questions:  1.  Explain  the  tangent  method  of  plotting  trav- 
erses, p.  465.  2.  If  the  closing  line  passes  through  the  first 
station  and  is  of  the  right  length  on  the  drawing,  what  addi- 
tional check  may  be  applied?  p.  465.  3.  When  a  traverse  has 
a  large  number  of  sides,  what  check  should  be  applied  at  every 
fourth  or  fifth  station?  p.  466,  §  503  (c). 


Exercise  P-5. 
Chord  Method  of  Plotting  Traverses. 

Reference:  Page  465,  §  503  (b). 

Directions:  Same  as  for  the  preceding  exercise  except  that 
the  table  made  out  in  the  note-book  corresponds  to  that  at  the 
bottom  of  p.  465.  It  may  also  be  advisable  to  plot  deflection 
angles  at  stations  where  the  interior  angles  are  very  obtuse. 

Problem:  Same  as  the  problem  in  Exercise  P-3  except  that 
that  the  chord  method  is  used  for  plotting  angles. 

Questions:  1.  Explain  the  chord  method  for  plotting  trav- 
erses, p.  465.  2.  Give  the  checks  to  be  employed  in  this 
method,  p.  466.  3.  Give  the  method  of  plotting  by  deflection 
angles,  p.  466. 


EXERCISES    IN    PLOTTING.  157 

Exercise  P-6. 
Plotting  Traverses  by  Bearings. 

(Tangent  Method.) 
Reference:  Page  467,  §  505. 

Directions:  I.  If  the  bearings  of  the  lines  are  not  given,  cal- 
culate them  from  the  angles  at  the  stations.  2.  Make  a  sketch 
in  the  note-book  showing  the  bearing  of  each  line  and  its  length. 
3.  Prepare  a  table  in  the  note-book  corresponding  to  that  at 
the  top  of  p.  469.  4.  Find  the  direction  of  each  line  from  its 
bearing  by  the  method  illustrated  in  Fig.  505  (a),  p.  468,  or 
Fig.  505  (b),  p.  469,  preferably  the  latter  method.  Whichever 
method  is  used  do  not  fail  to  test  the  square  and  to  mark  each 
line  as  soon  as  obtained  with  its  letters  or  its  numbers  as  shown 
in  the  figures  referred  to  above.  5.  Plot  the  polygon  in  any 
position  which  will  bring  it  wholly  within  the  limits  of  the  paper, 
by  transferring  the  direction  of  each  line  of  the  polygon  to  its 
proper  place  in  the  plot.  Check  each  angle  of  the  polygon 
roughly  as  soon  as  it  is  obtained,  using  the  protractor  for  this 
purpose.  6.  Apply  the  usual  tests  to  the  closing  line. 

Problem:  Same  as  the  problem  in  Exercise  P-3  except  that 
the  sides  of  the  polygon  are  plotted  from  their  bearings  by  the 
tangent  method. 

Questions:  1.  Explain  the  general  method  of  plotting  trav- 
erses by  bearings,  p.  467.  2.  What  bearings  are  plotted?  See 
Note,  p.  467.  3.  Give  two  general  methods  of  procedure, 
p.  467.  4.  In  either  method  what  is  the  most  convenient 
meridian  to  assume?  p.  467.  5.  When  is  it  convenient  to  use 
a  T-square  with  an  adjustable  head?  p.  468.  6.  Explain  the 
tangent  method  of  plotting  bearings,  p.  468.  7.  Explain  the 
corresponding  modified  method,  p.  469.  8.  Explain  the  chord 
method  of  plotting  bearings,  p.  469.  9.  Explain  the  corre- 
sponding modified  method,  p.  470.  10.  Give  the  checks  to  be 
employed,  p.  471.  11.  Give  one  of  the  chief  objections  to 
plotting  traverses  by  bearings,  p.  471.  12.  To  what  kind  of 
work  is  this  method  best  suited? 


158         EXERCISES  IN  PLOTTING. 

Exercise  P-7. 
Plotting  Traverses  by  Bearings. 

(Chord  Method.) 

Reference:    Page  469,  §  505  (c)  and  §  505  (e). 

Directions:  This  exercise  might  be  made  exactly  like  the 
preceding  exercise,  using  the  chord  method  instead  of  the  tangent 
method  in  plotting  bearings.  This  would  involve  little  that  is 
new,  hence  it  is  better  to  employ  the  method  of  §  505  (e),  p.  470, 
drawing  a  new  meridian  at  each  station.  Follow  the  directions 
of  the  preceding  exercise  except  where  they  conflict  with  the 
method  used  in  this  exercise. 

Problem:  Same  as  the  problem  in  Exercise  P-3  except  that 
the  sides  of  the  polygon  are  plotted  from  their  bearings,  a  ref- 
erence meridian  being  drawn  at  each  station  and  the  correspond- 
ing bearing  plotted  by  the  chord  method. 

Questions:  1.  Explain  the  method  of  plotting  bearings  from 
a  reference  meridian  at  each  station,  p.  470.  2.  Compare  this 
method  with  the  method  of  the  preceding  exercise.  3.  Outline 
another  method  sometimes  used  for  large  maps.  p.  471. 
4.  What  is  the  advantage  of  this  method? 

Exercise  P-8. 
Plotting  Traverses  by  Azimuths. 

Reference:  Page  471,  §  506. 

Directions:  1.  Change  the  bearings  of  the  sides  of  the  poly- 
gon in  the  preceding  exercise  to  azimuths.  2.  Make  a  free- 
hand sketch  in  the  note-book,  giving  the  azimuth  and  length 
of  each  line,  and  the  angle  which  will  be  plotted  at  each  station. 
3.  Use  either  the  tangent  or  chord  method  for  plotting  the 
angles,  preparing  in  advance  a  table  of  tangents  or  of  chords  to 
correspond.  Apply  the  usual  checks  throughout  the  work. 

Problem:  Same  as  the  preceding  exercise  except  azimuths 
are  plotted  instead  of  bearings.  As  this  in  itself  involves  little 
that  is  new,  it  is  desirable  to  use  a  method  of  plotting  not 
employed  in  either  of  the  two  preceding  problems.  For  example, 
the  azimuths  may  be  plotted  by  the  tangent  method  from 
meridians  drawn  through  the  stations. 


EXERCISES    IN    PLOTTING.  159 

Exercise  P-9. 
Plotting  Traverses  by  Latitudes  and  Departures. 

Reference:  Pages  471  to  475,  §  507. 

Directions:  Follow  the  method  of  procedure  outlined  on 
p.  472,  §  507  (b),  observing  also  the  practical  suggestions  at  the 
top  of  p.  475. 

Problem:  Same  as  the  problem  in  Exercise  P-3  except  that  the 
polygon  is  plotted  by  the  method  of  latitudes  and  departures. 

Questions:  1.  What  bearings  are  used  in  computing  latitudes 
and  departures,  calculated  or  magnetic?  p.  471.  2.  Without 
going  into  detail,  what  is  the  general  method  of  plotting  by 
latitudes  and  departures?  p.  471.  3.  Why  is  the  most  west- 
erly station  the  most  convenient  reference  point?  p.  471. 
4.  Could  any  other  reference  point  be  used?  5.  If  azimuths 
are  given  in  field  notes  instead  of  bearings,  is  it  necessary  to 
reduce  them  to  bearings  before  calculating  latitudes  and  depar- 
tures? p.  472.  6.  Explain  three  different  methods  of  deter- 
mining which  is  the  most  westerly  station,  p.  472.  7.  Outline 
in  detail  the  general  method  of  plotting  by  latitudes  and  depar- 
tures, p.  472.  8.  What  is  the  object  in  using  a  reference- 
rectangle  and  measuring  from  the  two  nearest  sides  to  locate  a 
point  instead  of  locating  it  by  coordinates  by  means  of  a 
T-square  and  triangles?  p.  473,  "  Caution."  9.  Give  practical 
suggestions  for  plotting  by  latitudes  and  departures  as  regards 
(1)  plotting  large  maps;  (2)  assuming  the  reference-rectangle 
so  that  no  side  is  horizontal  or  vertical;  (3)  testing  the  rec- 
tangle; (4)  plotting  each  station  by  its  latitude  and  departure 
from  the  preceding  station,  and  the  advantage  of  this  method; 
(5)  advantage  of  drawing  the  traverse  lines  so  that  they  stop 
just  short  of  each  station,  p.  475.  10.  What  checks  may  be 
employed  in  this  method  of  plotting?  p.  475. 

Methods  of  Plotting  Traverses  Compared:  1.  Compare  the 
tangent  method  and  the  chord  method,  p.  475.  2.  What  is 
the  chief  advantage  in  plotting  direct  angles  or  deflection 
angles  instead  of  bearings  or  azimuths?  p.  475.  3.  What  are 
some  of  the  disadvantages  of  the  direct  angle  method?  p.  475. 
4.  When  may  the  method  of  plotting  by  bearings  be  used? 
p.  476.  5.  What  are  the  advantages  of  plotting  by  latitudes 
and  departures?  p.  476. 


160          EXERCISES  IN  PLOTTING. 

Exercise  P-10. 
Plotting  the  Survey  on  Page  184. 

Note:  It  will  be  found  that  the  plotting  of  this  survey  is  exceedingly 
good  practice,  as  it  involves  nearly  all  the  common  methods  of  locating 
points  which  are  used  in  the  field.  If  desired,  recitations  Q-l  to  Q-4  may 
be  held  in  connection  with  this  exercise. 

Reference:  Comments  on  the  survey  are  given  on  p.  184;  com- 
ments on  the  notes  on  p.  185.  The  notes  themselves,  however, 
are  given  on  the  inset  sheet  opposite  to  p.  190,  Illustration  V. 

Directions:  1.  Plot  the  transit  lines  first,  using  one  of  the 
trigonometric  methods.  2.  Plot  the  details,  using  the  scale  and 
protractor. 

Problem:  Plot  the  survey  shown  on  the  inset  sheet  opposite 
p.  190,  Illustration  5.  Choose  a  scale  as  large  as  practicable  and 
still  have  the  map  fall  within  the  limits  of  the  paper. 


GROUP  Q. 

QUESTIONS    PERTAINING  TO  MAPPING. 


Plotting  Maps  from  Field  Notes. 

(Introductory). 

In  most  courses  in  surveying  students  are  required  to  plot 
maps  from  their  own  notes  taken  in  the  field.  The  preliminary 
drill  in  plotting  having  been  completed  and  this  work  of  plotting 
field  notes  having  been  begun,  it  is  well  to  hold  recitations  from 
time  to  time  on  tl^at  part  of  the  mapping  in  which  the  student  is 
engaged.  Thus,  for  example,  before  beginning  to  work  up  the 
notes  preparatory  to  plotting,  it  is  well  to  cover  the  ground  out- 
lined by  the  questions  in  Exercise  Q-l.  Before  beginning  to 
plot,  the  questions  in  Exercises  Q-2  and  Q-3  may  be  discussed. 
Before  beginning  to  plot  details,  Exercise  Q-4  may  be  taken  up, 
and  when  the  map  is  finally  completed  in  pencil  and  ready  to 
ink,  questions  on  finishing  the  map  may  be  discussed. 

Exercise  Q-l. 

Working  Up  Field  Notes  Preparatory  to  Plotting. 

Questions:  1.  What  is  one  of  the  first  things  to  do  in  working 
up  notes?  p.  477.  2.  In  addition  to  saving  time  what  other 
object  is  there  in  getting  together  all  data  and  in  making  all  the 
preliminary  calculations  before  beginning  to  plot?  p.  473.  3. 
When  is  it  most  necessary  to  correct  field  measurements?  p.  478. 
4.  What  are  some  of  the  corrections  applied  to  linear  measure- 
ments? to  angular  measurements?  p.  478.  5.  For  what  purpose 
are  measurements  adjusted?  p.  478.  6.  How  may  linear  meas- 
urements be  adjusted?  angular  measurements?  p.  478.  7.  It  is 
often  best  not  to  follow  any  rule  in  adjusting  angles.  How  is  this 
illustrated  by  the  survey  on  p.  390?  p.  479.  8.  In  work  of  great 
precision  how  are  observed  values  adjusted?  p.  479.  9.  What  can 
you  say  regarding  the  calculation  of  bearings:  for  purposes  of  plot- 
ting; true  bearings;  use  of  adjusted  values  in  angles;  bearings  in 

161 


162         QUESTIONS    PERTAINING    TO    MAPPING. 

compass  surveys?  p.  479.  10.  What  methods  are  used  for 
supplying  missing  data  and  what  is  the  disadvantage  in  the  use  of 
these  methods?  p.  480.  11.  Explain  the  method  of  reducing 
stadia  notes  by  the  use  of  reduction  tables;  by  means  of  a  dia- 
gram.* p.  481.  12.  Why  should  the  abridged  method  of 
multiplication  be  used  in  connection  with  reduction  tables? 
13.  Summarize  the  first  five  or  six  steps  in  preparing  data  for 
plotting,  p.  483.  14.  Give  the  additional  steps,  p.  484,  for 
(a)  protractor  method ;  (b)  tangent  method ;  (c)  chord  method ; 
(d)  latitude  and  departure  method;  (e)  azimuth  method. 


Exercise  Q-2. 
Plotting  the  Map. 

(General  Methods  and  Suggestions.) 

Questions:  1.  What  is  the  best  kind  of  paper  for  map  work? 
p.  485.  2.  What  is  the  best  paper  for  maps  that  are  to  be  tinted ; 
for  maps  to  be  reproduced?  p.  485.  3.  What  are  the  advantages 
and  disadvantages  of  the  different  kinds  of  blue  print  paper? 
p.  485.  4.  What  are  the  most  essential  requirements  for  draw- 
ing instruments?  p.  486.  5.  Give  some  of  the  precautions  to  be 
taken  in  accurate  plotting,  p.  486.  6.  What  effect  has  the 
shrinkage  of  the  paper  and  how  may  shrinkage  be  partly  avoided? 
p.  486.  7.  Why  should  maps  be  kept  flat?  p.  487.  8.  Give  the 
general  methods  employed  in  mapping,  p.  487.  9.  Give  the 
general  method  of  procedure,  p.  487.  10.  What  are  the  most 
common  scales  for  ordinary  maps?  p.  488.  11.  Why  are  not  the 
scales  of  70  and  90  ft.  to  the  inch  commonly  used?  p.  488. 
12.  What  is  the  so-called  natural  scale  and  what  are  some  of  the 
scales  used  for  government  work?  p.  488.  13.  Give  some  of  the 
primary  considerations  in  choosing  a  scale  and  illustrate  by 
examples,  p.  489.  14.  Give  some  of  the  common  scales  used: 
for  preliminary  surveys  of  railroads;  maps  of  mines  and  mining 
claims;  maps  for  architects,  p.  489.  15.  What  are  the  advan- 
tages of  the  scales  1  in.  =  20  ft.,  1  in.  =  40  ft.,  and  1  in.  =  80  ft.? 
p.  489.  16.  What  are  some  of  the  considerations  which  some- 
times determine  the  size  of  the  sheet?  p.  489.  17.  How  does  the 
arrangement  of  the  map  affect  the  size  of  the  sheet?  p.  489. 

*  If  desired,  the  student  may  be  required  to  construct  a  diagram. 


QUESTIONS    PERTAINING    TO   MAPPING.         163 

18.  How  may  the  shape  and  extent  of  a  survey  be  determined 
roughly?  p.  489.  19.  Give  two  general  rules  for  choosing  the 
scale  for  a  map.  p.  490.  20.  Why  is  it  advantageous  to  adopt  a 
small  scale  for  topographic  maps?  p.  490.  21.  What  is  the 
object  in  sometimes  drawing  maps  of  the  same  territory  to  dif- 
ferent scales?  p.  490.  22.  What  arrangement  of  the  map  is 
desirable  as  regards  points  of  the  compass?  p.  490.  23.  Why 
is  this  arrangement  seldom  economical?  24.  What  effect  has 
the  natural  approach  to  a  piece  of  property  on  the  arrangement 
of  the  map?  p.  490.  25.  What  is  usually  the  first  step  in  begin- 
ning a  map?  p.  490.  26.  Where  do  you  begin  to  plot  a  map 
and  why  work  half  way  around  a  polygon  in  either  direction? 
p.  491.  27.  Give  suggestions  for  assuming  the  first  line.  p.  491. 

28.  When  it  is  desired  to  economize  space  and  the  map  is 
plotted   by  latitudes  and   departures   how  would  you  proceed 
in  assuming  a  reference-meridian,  or  reference-rectangle?  p.  491. 

29.  When  is  a  preliminary  plot  unnecessary?  p.  491. 


Exercise  Q-3. 
Plotting  Traverses. 

(Review.) 

Questions:  1.  To  what  do  the  different  methods  of  plotting 
traverses  correspond?  p.  492.  2.  In  plotting  traverses  when  is 
the  protractor  used?  3.  What  are  the  other  methods  used  for 
plotting  traverses?  4.  Why  should  traverse  lines  be  plotted 
accurately?  5.  Summarize  five  methods  of  plotting  transit 
lines,  giving  the  checks  used  in  each:  (1)  each  line  plotted  from 
the  preceding  line,  p.  492;  (2)  each  line  plotted  by  deflection 
angle,  p.  493;  (3)  each  line  plotted  from  its  bearing,  p.  493; 
(4)  each  line  plotted  from  its  azimuth,  p.  493;  (5)  transit  lines 
plotted  from  latitudes  and  departures,  p.  493.  6.  Give  the 
methods  of  checking  linear  measurements:  (1)  any  straight  line; 
(2)  comparing  the  lengths  of  lines  with  corresponding  distances 
in  field  notes;  (3)  checking  lines  of  a  traverse;  (4)  checking  two 
points  by  indirect  measurements.  7.  Give  the  checks  for  angles : 
(1)  when  laid  off  with  a  protractor;  (2)  test  for  two  or  more 
adjacent  angles;  (3)  check  for  angles  plotted  by  trigonometric 
method;  (4)  checking  angles  between  traverse  lines.  8.  Answer 


164         QUESTIONS    PEKTAINING    TO    MAPPING. 

question  on  p.  495.  9.  Give  combination  checks:  (1)  for 
a  reference-rectangle;  (2)  for  a  closed  traverse;  (3)  for  extra 
distances  taken  in  the  field,  p.  495.  10.  Give  methods  of  running 
down  errors,  p.  495:  (1)  when  the  error  of  closure  is  parallel  or 
perpendicular  to  some  line  in  the  traverse;  (2)  when  a  traverse 
has  been  plotted  by  direct  angles;  (3)  when  the  direction  of  the 
closing  line  is  found  to  be  incorrect;  (4)  when  lines  have  been 
plotted  by  bearings  or  azimuths;  (5)  when  a  point  is  wrong  and 
the  mistake  not  easily  found;  (6)  effect  of  long  lines  and  lines 
north  and  south  or  east  and  west.  1 1 .  Give  the  different  methods 
of  plotting  a  triangulation  net.  p.  491. 


Exercise  Q-4. 
Plotting  Details. 

Questions:  1.  Give  the  methods  of  plotting  points  located  by 
angles  and  distances,  p.  496.  2.  What  precautions  should  be 
taken  to  avoid  confusion?  3.  Give  the  methods  of  plotting 
points  located  by  angles.  4.  Give  the  method  of  plotting  points 
by  linear  methods  only.  5.  How  may  the  straightness  of  a  line 
located  by  offsets  be  tested?  6.  Give  general  suggestions  for 
keeping  the  drawing  free  from  unnecessary  lines,  p.  496;  for 
testing  check  distances;  for  plotting  important  points  at  a 
station;  for  plotting  doubtful  points,  p.  497.  7.  Explain  the 
graphic  method  of  interpolating  contours,  p.  497.  8.  Why,  as 
a  rule,  will  a  point  interpolated  from  two  given  points  be  dif- 
ferent if  interpolated  between  two  other  points.  Remark, 
p.  497.  9.  Explain  the  tracing  cloth  method  of  interpolating 
contours,  p.  497.  10.  Give  suggestions  for  the  use  of  this 
method,  p.  498.  11.  Describe  a  home-made  device  for  inter- 
polating contours,  p.  498.  12.  What  determines  the  accuracy 
required  in  plotting?  and  give  illustrations,  p.  499.  13.  What 
contributes  to  speed  in  plotting?  p.  499.  14.  Give  the  different 
methods  of  copying  and  transferring  maps.  p.  500.  15.  Which 
methods  are  used  for  copying  to  a  different  scale  from  that  of  the 
original  map.  p.  501. 


QUESTIONS    PERTAINING    TO    MAPPING.         165 

Exercise  Q-5. 
Finishing  the  Map. 

Questions:  1.  In  finishing  a  map  what  are  some  of  the  specifi- 
cations for  workmanship?  p.  502.  2.  What  in  general  should 
appear  on  a  map?  p.  502.  3.  When  is  the  scale  of  the  map 
shown  by  a  drawing  instead  of  being  given  in  figures?  p.  502. 
4.  Is  a  magnetic  meridian  always  shown?  p.  502.  5.  What 
are  the  most  important  requirements  for  an  ordinary  property 
map?  p.  502.  6.  What  are  some  of  the  additional  requirements 
prescribed  by  law  in  some  states?  Remark,  p.  503.  7.  Give 
some  of  the  requirements  for  topographic  maps.  p.  503.  8.  Give 
some  of  the  things  which  should  appear  on  a  map  made  for  an 
architect,  p.  211.  9.  Give  the  general  method  of  procedure  in 
finishing  a  map.  p.  503.  10.  Give  suggestions  for  arrangement 
of  (a)  border  lines,  p.  504;  (b)  lettering,  p.  505;  (c)  titles,  p.  505; 

(d)  names  of  streets,  streams,  property  owners,   etc.,   p.   505; 

(e)  give  additional  suggestions  for  arrangement,  p.  505. 

Questions  on  Inking:  1.  Give  suggestions  for  the  use  of  a 
ruling  pen  as  regards  (1)  producing  clear-cut  lines,  p.  440; 
(2)  method  of  holding  the  pen,  p.  440;  (3)  adjusting  the  nibs 
of  the  pen,  p.  441;  (4)  cleaning  the  nibs;  (5)  sharpening  the 
pen;  (6)  method  of  inking  straight  lines  (Suggestions  (5),  (6), 
and  (7),  p.  446);  (7)  order  of  inking  straight  lines  and  circles, 
p.  447;  (8)  inking  lines  that  meet  in  a  point,  p.  447;  (9)  inking 
wide  lines,  p.  447;  (10)  mixing  india  ink,  p.  447.  2.  Give 
additional  suggestions  for  inking  as  regards  (1)  order  of  inking 
lines,  p.  506;  (2)  inking  edges  of  streams  and  similar  indefinite 
lines,  p.  506;  (3)  inking  traverse  lines,  p.  506;  (4)  inking 
broken  lines.  3.  Give  the  method  of  outline  shading,  p.  506. 
4.  Give  suggestions  for  the  use  of  colored  inks.  p.  506. 

Questions  on  Tracing:  1.  Give  general  suggestions  for  tracing 
as  regards  (1)  which  side  of  the  cloth  to  use,  p.  451;  (2)  prep- 
aration of  the  tracing  cloth,  p.  451 ;  (3)  effect  of  too  fine  lines 
and  figures  on  the  blue  print,  p.  451;  (4)  precautions  to  be 
taken  in  erasing  on  tracing  cloth,  p.  452;  (5)  inserting  new 
pieces  of  cloth,  p.  452;  (6)  effect  of  moisture  on  tracing  cloth, 
p.  452;  (7)  use  of  tracing  paper  instead  of  tracing  cloth,  p.  452; 
(8)  best  ink  to  use,  p.  452;  (9)  method  of  cleaning  a  tracing, 


166         QUESTIONS    PERTAINING    TO    MAPPING. 

p.  452.  2.  What  are  the  printing  qualities  of  different  colored 
inks?  p.  507.  3.  How  may  tracings  be  colored  with  pencils? 
p.  507.  4.  How  should  streams  and  shore  lines  be  colored? 
p.  507.  5.  Give  method  of  lettering  tracings  by  shifting  let- 
ters underneath,  p.  517. 

Questions  on  Lettering:  1.  Upon  what  does  good  lettering 
mostly  depend?  p.  507.  2.  What  defects  in  lettering  are  the 
least  excusable?  p.  508.  3.  Give  some  suggestions  as  regards 
style  of  letters,  p.  508.  4.  Give  general  method  of  lettering, 
p.  509.  5.  Give  suggestions  as  regards  the  size  of  letters, 
p.  509.  6.  Give  suggestions  as  regards  the  proportions  of 
letters,  p.  510.  7.  Give  suggestions  for  penciling  the  letters 
as  regards  (1)  use  of  guide  lines,  p.  510;  (2)  estimating  the 
unit  for  proportioning;  (3)  blocking  out  letters;  (4)  two  things 
to  observe  in  drawing  letters,  p.  511;  (5)  devices  for  lettering 
on  tracing  cloth,  p.  511.  8.  Give  the  most  important  points  to 
be  remembered  in  the  construction  of  the  various  letters.* 
p.  511.  9.  Give  suggestions  for  inking  letters  as  regards:  pens 
used,  p.  515;  inking  outlines  of  letters;  filling  in;  touching  up 
imperfect  corners;  testing  the  pen;  precautions  for  keeping  the 
ink.  10.  What  are  the  most  common  defects  in  lettering? 
p.  516.  11.  Give  suggestions  for  spacing  letters  on  paper;  on 
tracings,  p.  516.  12.  Give  general  suggestions  for  lettering 
maps  as  regards  (1)  general  arrangement,  p.  517;  (2)  letter- 
ing curved  streets  or  winding  rivers;  (3)  arrangement  of  two 
lines  that  are  not  centered;  (4)  positions  of  names  and  descrip- 
tions; (5)  printing  values  of  small  angles  and  of  a  decimal  of 
a  foot;  (6)  distinguishing  between  angular  measurements  and 
linear  measurements,  p.  518;  (7)  indicating  the  forward  bear- 
ing for  a  line.  13.  Give  six  different  methods  of  making  letter- 
ing more  prominent,  p.  518. 

Finishing  Topographic  Maps:  1.  Give  suggestions  for  draw- 
ing contour-lines  as  regards  (1)  color  of  ink,  p.  518;  (2)  width 
of  lines  and  kind  of  pen  used;  (3)  which  contours  are  accentu- 
ated; (4)  marking  elevations  of  accentuated  contours;  (5) 
breaks  in  contour-lines,  p.  519;  (6)  representing  intermediate 
contours.  2.  What  are  some  of  the  common  mistakes  in 
drawing  contours?  p.  519,  p.  338.  3.  Give  suggestions  for 

*  This  study  of  the  Gothic  capitals  is  best  made  in  connection  with  a 
regular  course  in  lettering,  or  at  least  in  separate  exercises  devoted  to 
practice  in  proportioning  letters. 


QUESTIONS    PERTAINING    TO    MAPPING.         167 

conventional  signs.*  p.  519.  4.  Give  method  of  drawing  small 
water  courses,  p.  519.  5.  Give  suggestions  for  water-lining, 
p.  522.  6.  Give  suggestions  for  section-lining,  p.  522. 

Questions  on  Tinting.  (See  p.  449.)  1.  Give  the  method  of 
mixing  the  tint.  2.  What  is  the  effect  of  pencil  lines?  p.  450. 

3.  Should  the  drawing  be  tinted  first  or  inked  first?     4.  Give 
suggestions   for  applying   the  tint.     p.  450.      5.    What    is    the 
secret  of  success  in  tinting?    p.  450.     6.    How  may  the  tint  be 
removed  from  outside  the  boundary  line?     7.    How  may  the 
surplus  tint  be  removed?     8.    Why  is  it  well  to  go  over  the 
surface  first  with  clean  water?  p.   451.     9.    What  is  the  best 
method  of  securing  a  dark  tint?     10.    To  what  is  tinting  on 
ordinary  maps  usually  confined?  p.  523.     11.   Give  some  of  the 
conventional  tints. 

Questions  on  Border-Lines  and  Titles:  1.  (p.  523.)  Give  general 
suggestions  for  drawing  border-lines  as  regards:  simplicity; 
size  of  rectangle;  width  of  heaviest  border-line;  method  of 
drawing  a  heavy  border-line.  2.  Where  is  the  best  place  for 
a  title?  3.  On  what  does  the  size  of  the  largest  letters  depend? 

4.  What  is  the  first  consideration  in  designing  a  title?     5.    Give 
suggestions  for:    arranging  subject-matter;    making  some  lines 
more   prominent   than   others;   centering   lines;    spacing   lines; 
making  lines  of  unequal  length;   styles  of  lettering.     6.    Should 
lower-case  letters  be  used?    p.  524.     7.   Is  it  well  to  make  part 
of  the  letters  inclined  and  part  upright?     8.    For  what  is  single- 
stroke    lettering   used?     9.    When   should   the   title    be   drawn 
freehand   and  when  with   instruments?     10.    Should  words  be 
abbreviated  in  a  title?     11.    How  may  a  title  be  centered  on 
tracing  cloth?     12.    What  are  some  of  the  mechanical  devices 
for  printing  titles?     13.   What  should  appear  in  a  title?  p.  525. 
14.    Give  the  general  method  of  procedure  in  constructing  a 
title,  p.  525. 

Questions  on  Meridian  Needles,  Scales,  etc.:  1.  How  is  the 
true  north  distinguished  from  the  magnetic  north?  p.  526. 
2.  How  is  the  direction  of  the  arrows  determined?  3.  Why 
should  the  magnetic  declination  be  given  in  figures,  if  given  at 
all?  4.  How  is  the  scale  usually  given?  5.  When  is  it  most 
necessary  to  represent  it  by  a  drawing,  and  what  is  the  chief 
advantage  of  this?  6.  What  is  the  purpose  of  keys  or  legends? 

*  A  plate  of  conventional  signs  may  well  be  drawn  either  in  a  separate 
exercise  or  in  connection  with  a  course  in  lettering. 


168         QUESTIONS    PERTAINING    TO    MAPPING. 

7.  When  should  explanatory  notes  be  used  and  where  should 
they  be  placed?  8.  How  may  the  paper  be  cleaned  when 
maps  are  finished;  how  may  tracings  be  cleaned?  9.  What 
are  some  of  the  things  that  should  be  stated  in  a  surveyor's 
certificate?  p.  527.  10.  By  looking  up  some  of  the  references 
on  p.  528,  give  the  most  essential  elements  of  a  good  filing 
system. 

Exercise  Q-6.* 
Profiles. 

Questions:  1.  In  plotting  profiles,  is  it  customary  to  use  the 
same  scale  for  laying  off  elevations  that  is  used  for  horizontal 
distances?  p.  529.  2.  When  does  a  profile  represent  a  true 
vertical  section  and  when  does  it  not?  p.  530.  3.  Why  are 
profiles  apt  to  be  misleading?  Remark,  p.  530.  4.  What  are 
the  three  standard  styles  of  profile  paper?  p.  530.  5.  Give 
suggestions  for  the  choice  of  scale,  p.  531.  6.  What  are  some 
of  the  most  convenient  combinations  of  papers  and  scales? 
p.  531.  7.  Give  the  method  of  working  up  notes  for  profiles, 
including  the  checks,  p.  531.  8.  Give  suggestions  for  method 
of  procedure  in  plotting  profiles  as  regards:  assuming  the  posi- 
tion and  elevation  of  base-line,  p.  532 ;  where  to  begin  the  pro- 
file; how  to  make  100-ft.  stations  fall  on  accentuated  vertical 
lines;  how  to  number  accentuated  lines,  vertical  and  horizontal; 
how  to  plot  points;  how  to  check  points.  9.  Give  additional 
suggestions  for:  two  men  working  to  advantage,  p.  533;  mark- 
ing points;  continuing  a  profile  which  runs  off  the  bottom  or 
top  of  the  paper;  avoiding  the  common  mistake  of  plotting 
turning-points  and  benches;  plotting  accurate  profiles;  making 
several  copies  of  profiles.  10.  Give  examples  of  the  method  of 
plotting  the  profiles  of  several  related  lines,  p.  533.  11.  Give 
the  method  of  laying  out  grades  and  vertical  curves  on  profile. 
p.  533.  12.  Give  suggestions  for  finishing  profiles  as  regards: 
representing  existing  surfaces  and  proposed  changes;  ruling 
the  profile  or  drawing  it  freehand ;  smoothing  out  sharp  angles ; 
inking  the  base-line ;  methods  of  marking  elevations ;  the  points 
at  which  elevations  should  be  marked;  marking  cut  or  fill; 
marking  rate  of  grade;  tinting  or  coloring  profiles;  method  of 
showing  different  materials.  13.  Give  suggestions  for  lettering 
profiles,  p.  535. 

*  Recitation  to  be  held  in  connection  with  an  exercise  in  plotting  profiles. 


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7 


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8 


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Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  00 

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Butts's  Civil  Engineer's  Field-book 16mo,  mor.  2  50 

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9 


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10 


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12 


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Compton's  First  Lessons  in  Metal  Working 12mo,  1  50 

Compton  and  De  Groodt's  Speed  Lathe 12mo,  1  50 

Coolidge's  Manual  of  Drawing 8vo,  paper,  1   00 

Coolidge  and  Freeman's  Elements  of  Geenral  Drafting  for  Mechanical  En- 
gineers  Oblong  4to,  2  50 

Cromwell's  Treatise  on  Belts  and  Pulleys 12mo,  1   50 

Treatise  on  Toothed  Gearing 12mo,  1  50 

Dingey's  Machinery  Pattern  Making 12mo,  2  00 

Durley's  Kinematics  of  Machines 8vo,  4  00 

Flanders's  Gear-cutting  Machinery Large  12mo,  3  00 

Flather's  Dynamometers  and  the  Measurement  of  Power 12mo,  3  00 

Rope  Driving 12mo,  2  00 

Gill's  Gas  and  Fuel  Analysis  for  Engineers 12mo,  1  25 

Goss's  Locomotive  Sparks 8vo,  2  00 

Greene's  Pumping  Machinery.      (In  Preparation.) 

Hering's  Ready  Reference  Tables  (Conversion  Factors) 16mo,  mor.  2  50 

*  Hobart  and  Ellis's  High  Speed  Dynamo  Electric  Machinery 8vo,  6  00 

Hutton's  Gas  Engine 8vo,  5  00 

Jamison's  Advanced  Mechanical  Drawing 8vo,  2  00 

Elements  of  Mechanical  Drawing 8vo,  2  50 

Jones's  Gas  Engine 8vo,  4  00 

Machine  Design; 

Part  I.      Kinematics  of  Machinery 8vo,  1   50 

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Kent's  Mechanical  Engineer's  Pocket-Book 16mo,  mor.  5  00 

Kerr's  Power  and  Power  Transmission 8vo,  2  00 

Kimball  and  Barr's  Machine  Design.      (In  Press.) 

Levin's  Gas  Engine.      (In  Press.) 8vo, 

Leonard's  Machine  Shop  Tools  and  Methods 8vo,  4  00 

*  Lorenz's  Modern  Refrigerating  Machinery.   (Pope,  Haven,  and  Dean).  .8vo,  4  00 
MacCord's  Kinematics;  or,  Practical  Mechanism 8vo,  5  00 

Mechanical  Drawing 4to,  4  00 

Velocity  Diagrams 8vo,  1  50 

MacFarland's  Standard  Reduction  Factors  for  Gases 8vo,  1  50 

Mahan's  Industrial  Drawing.      (Thompson.) 8vo,  3  50 

Mehrtens's  Gas  Engine  Theory  and  Design Large  12mo,  2  50 

Oberg's  Handbook  of  Small  Tools Large  12mo,  3  00 

*  Parshall  and  Hobart's  Electric  Machine  Design.  Small  4to,  half  leather,  12  50 

Peele's  Compressed  Air  Plant  for  Mines 8vo,  3  00 

Poole's  Calorific  Power  of  Fuels 8vo,  3  00 

*  Porter's  Engineering  Reminiscences,  1855  to  1882 8vo,  3  00 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  00 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  00 

Richards's  Compressed  Air .  12mo,  1  50 

Robinson's  Principles  of -Mechanism 8vo,  3  00 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  00 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  00 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  00 

Sorel's  Carbureting  and  Combustion  in  Alcohol  Engines.      (Woodward  and 

Preston.) Large  12mo,  3  00 

Stone's  Practical  Testing  of  Gas  and  Gas  Meters 8vo,  3  50 

13 


Thurston's  Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics. 

12mo,   $1  00 

Treatise  on  Friction  and  Lost  Work  in  Machinery  and  Mill  Work.  .  .8vo,  3  00 

*  Tillson's  Complete  Automobile  Instructor 16mo,  1  50 

*  Titsworth's  Elements  of  Mechanical  Drawing Oblong  8vo,  1  25 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

*  Waterbury's  Vest  Pocket  Hand-book  of  Mathematics  for  Engineers. 

2|X5f  inches,  mor.  1  00 
Weisbach's    Kinematics    and    the    Power    of   Transmission.      (Herrmann — 

Klein.) ^ 8vo,  5  00 

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Wood's  Turbines 8vo,  2  50 


MATERIALS    OF   ENGINEERING. 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering 8vo,  7  50 

Church's  Mechanics  of  Engineering 8vo,  6  00 

*  Greene's  Structural  Mechanics 8vo,  2  50 

*  Holley's  Lead  and  Zinc  Pigments Large  12mo  3  00 

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Steels,  Steel-Making  Alloys  and  Graphite Large  12mo,  3  00 

Johnson's  (J.  B.)  Materials  of  Construction 8vo,  6  00 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Maire's  Modern  Pigments  and  their  Vehicles 12mo,  2  00 

Martens's  Handbook  on  Testing  Materials.      (Henning.) 8vo,  7  50 

Maurer's  Techincal  Mechanics 8vo,  4  00 

Merriman  s  Mechanics  of  Materials 8vo,  5  00 

*  Strength  of  Materials 12mo,  1  00 

Metcalf's  Steel.      A  Manual  for  Steel-users 12mo,  2  00 

Sabin's  Industrial  and  Artistic  Technology  of  Paint  and  Varnish 8vo,  3  00 

Smith's  ((A.  W.)  Materials  of  Machines 12mo,  1  00 

Smith's  (H.  E.)  Strength  of  Material 12mo, 

Thurston's  Materials  of  Engineering 3  vols.,  8vo,  8  00 

Part  I.      Non-metallic  Materials  of  Engineering, 8vo,  2  00 

Part  II.     Iron  and  Steel 8vo,  3  50 

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Constituents 8vo,  2  50 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  00 

Treatise  on    the    Resistance    of    Materials    and    an    Appendix    on    the 

Preservation  of  Timber 8vo,  2  00 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  00 


STEAM-ENGINES    AND   BOILERS. 

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Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.).  .  .  ..12mo.  1  50 

Chase's  Art  of  Pattern  Making 12mo,  2  50 

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Dawson's  "'Engineering"  and  Electric  Traction  Pocket-book.  ..  .  16mo,  mor.  5  00 

Ford's  Boiler  Making  for  Boiler  Makers 18mo,  1  00 

*  Gebhardt's  Steam  Power  Plant  Engineering 8vo,  6  00 

Goss's  Locomotive  Performance 8vo,  5  00 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy.. 12mo,  2  00 

Hutton's  Heat  and  Heat-engines 8vo.  5  00 

Mechanical  Engineering  of  Power  Plants 8vo,  5  00 

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14 


Kneass's  Practice  and  Theory  of  the  Injector 8vo,  $1  50 

MacCord's  Slide-valves 8vo,  2  00 

Meyer's  Modern  Locomotive  Construction 4to,  10  00 

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Peabody's  Manual  of  the  Steam-engine  Indicator 12mo,  1  50 

Tables  of  the  Properties  of  Steam  and  Other  Vapors  and  Temperature- 
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Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  00 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

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Reagan's  Locomotives:  Simple,  Compound,  and  Electric.     New  Edition. 

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Smart's  Handbook  of  Engineering  Laboratory  Practice 12mo,  2  50 

Snow's  Steam-boiler  Practice 8vo,  3  00 

Spangler's  Notes  on  Thermodynamics 12mo,  1  00 

Valve-gears 8vo,  2  50 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  00 

Thomas's  Steam-turbines 8vo,  4  00 

Thurston's  Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indi- 
cator and  the  Prony  Brake 8vo,  5  00 

Handy  Tables 8vo,  1  50 

Manual  of  Steam-boilers,  their  Designs  .Construction,  and  Operation  8vo,  5  00 

Manual  of  the  Steam-engine.. 2vols.,   8vo,  10  00 

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Wehrenfennig's    Analysis  and  Softening  of  Boiler  Feed-water.     (Patterson). 

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Weisbach's  Heat,  Steam,  and  Steam-engines.      (Du  Bois.) 8vo,  5  00 

Whitham's  Steam-engine  Design 8vo,  5  00 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines.  .  .8vo,  4  00 


MECHANICS    PURE   AND    APPLIED. 

Church's  Mechanics  of  Engineering 8vo,  6  00 

Notes  and  Examples  in  Mechanics .' 8vo,  2  00 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools  .12mo,  1   50 
Du  Bois's  Elementary  Principles  of  Mechanics: 

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Vol.  II.     Statics 8vo,  4  00 

Mechanics  of  Engineering.      Vol.     I Small  4to,  7  50 

Vol.  II Small  4to,  10  00 

*  Greene's  Structural  Mechanics 8vo,  2  50 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle. 

Large  12mo,  2  00 

*  Johnson's  (W.  W.)  Theoretical  Mechanics 12mo,  3  00 

Lanza's  Applied  Mechanics 8vo,  7  50 

*  Martin's  Text  Book  on  Mechanics,  Vol.  I,  Statics 12mo,  1   25 

*  Vol.  II,  Kinematics  and  Kinetics.  12mo,  1   50 

Maurer's  Technical  Mechanics 8vo,  4  00 

*  Merriman's  Elements  of  Mechanics 12mo,  1   00 

Mechanics  of  Materials 8vo,  5  00 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  00 

Robinson's  Principles  of  Mechanism 8vo,  3  00 

Sanborn's  Mechanics  Problems Large  12mo,  1  50 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  00 

Wood's  Elements  of  Analytical  Mechanics 8vo,  3  00 

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15 


MEDICAL. 

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Defren.) 8vo, 

von  Bchring's  Suppression  of  Tuberculosis.      (Bolduan.) 12mo,     1 

Bolduan's  Immune  Sera 12mo,     1 

Bordet's  Studies  in  Immunity.      (Gay).      (In  Press.) 8vo, 

Davenport's  Statistical  Methods  with  Special  Reference  to  Biological  Varia- 
tions  16mo,  mor.  1 

Ehrlich's  Collected  Studies  on  Immunity.      (Bolduan.) 8vo, 

*  Fischer's  Physiology  of  Alimentation Large  12mo, 

de  Fursac's  Manual  of  Psychiatry.      (Rosanoff  and  Collins.)..  .  .Large  12mo, 

Hammarsten's  Text-book  on  Physiological  Chemistry.      (Mandel.) 8vo, 

Jackson's  Directions  for  Laboratory  Work  in  Physiological  Chemistry.  .8vo, 

Lassar-Cohn's  Practical  Urinary  Analysis.      (Lorenz.) 12mo, 

Mandel's  Hand-book  for  the  Bio-Chemical  Laboratory 12mo, 

*  Pauli's  Physical  Chemistry  in  the  Service  of  Medicine.      (Fischer.)  ..12mo, 

*  Pozzi-Escot's  Toxins  and  Venoms  and  their  Antibodies.      (Cohn.).  .  12mo, 

Rostoski's  Serum  Diagnosis.     (Bolduan.) 12mo,     1 

Ruddiman's  Incompatibilities  in  Prescriptions 8vo,     2 

Whys  in  Pharmacy 12mo,  1 

Salkowski's  Physiological  and  Pathological  Chemistry.      (Orndorff.)   . .  .  .8vo,  2 

*  Satterlee's  Outlines  of  Human  Embryology 12mo,  1 

Smith's  Lecture  Notes  on  Chemistry  for  Dental  Students 8vo,  2 

*  Whipple's  Tyhpoid  Fever Large  12mo,  3 

Woodhull's  Notes  on  Military  Hygiene 16mo,  1 

*  Personal  Hygiene 12mo,      1 

Worcester  and  Atkinson's  Small  Hospitals  Establishment  and  Maintenance, 
and  Suggestions  for  Hospital  Architecture,  with  Plans  for  a  Small 
Hospital 12mo,  1 


METALLURGY. 

Betts's  Lead  Refining  by  Electrolysis &vo,     4 

Bolland's  Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  used 

in  the  Practice  of  Moulding 12mo, 

Iron  Founder 12mo, 

Supplement 12mo, 

Douglas's  Untechnical  Addresses  on  Technical  Subjects 12mo, 

Goesel's  Minerals  and  Metals:  A  Reference  Book 16mo,  mor. 

*  Iles's  Lead-smelting 12mo, 

Johnson's    Rapid    Methods   for    the   Chemical    Analysis   of   Special    Steels, 

Steel-making  Alloys  and  Graphite Large  12mo,     3 

Keep's  Cast  Iron 8vo,     2 

Le  Chatelier's  High-temperature  Measurements.     (Boudouard — Burgess.) 

12mo,     3 

Metcalf's  Steel.      A  Manual  for  Steel-users 12mo,     2 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.      (Waldo.).  .  12mo,      2 

Ruer's  Elements  of  Metallography.      (Mathewson) 8vo, 

Smith's  Materials  of  Machines 12mo,      1 

Tate  and  Stone's  Foundry  Practice 12mo,      2 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,     8 

Part  I.       Non-metallic  Materials  of  Engineering,  see  Civil  Engineering, 
page  9. 

Part  II.     Iron  and  Steel 8vo,     3 

Part  III.  A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,     2 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,     3 

West's  American  Foundry  Practice 12mo,     2 

Moulders'  Text  Book 12mo,     2 

16 


MINERALOGY. 

Baskerville's  Chemical  Elements.      (In  Preparation.). 

Boyd's  Map  of  Southwest  Virginia Pocket-book  form.  $2  00 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo,  1   50 

Brush's  Manual  of  Determinative  Mineralogy.      (Penfield.) 8vo,  4  00 

Butler's  Pocket  Hand-book  of  Minerals 16mo,  mor.  3  00 

Chester's  Catalogue  of  Minerals 8vo,  paper,     1  00 

Cloth,  1  25 

*  Crane's  Gold  and  Silver 8vo,  5  00 

Dana's  First  Appendix  to  Dana's  New  "  System  of  Mineralogy  ".  .  Large  8vo,  1  00 
Dana's  Second  Appendix  to  Dana's  New  "System  of  Mineralogy." 

Large  8vo, 

Manual  of  Mineralogy  and  Petrography 12mo,  2  00 

Minerals  and  How  to  Study  Them 12mo,  1  50 

System  of  Mineralogy Large  8vo,  half  leather,  12  50 

Text-book  of  Mineralogy 8vo,  4  00 

Douglas's  Untechnical  Addresses  on  Technical  Subjects 12mo,  1  00 

Eakle's  Mineral  Tables 8vo,  1  25 

Eckel's  Stone  and  Clay  Products  Used  in  Engineering.      (In  Preparation). 

Goesel's  Minerals  and  Metals:  A  Reference  Book 16mo,  mor.  3  00 

Groth's  Introduction  to  Chemical  Crystallography  (Marshall) 12mo,  1  25 

*  Hayes's  Handbook  for  Field  Geologists 16mo,  mor.  1  50 

Iddings's  Igneous  Rocks 8vo,  5  00 

Rock  Minerals 8vo,  5  00 

Johannsen's  Determination  of  Rock-forming  Minerals  in  Thin  Sections.  8vo, 

With  Thumb  Index  5  00 

*  Martin's  Laboratory    Guide    to    Qualitative    Analysis    with    the    Blow- 

pipe  12mo,  60 

Merrill's  Non-metallic  Minerals.  Their  Occurrence  and  Uses 8vo.  4  00 

Stones  for  Building  and  Decoration 8vo.  5  00 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 
Tables  of   Minerals,   Including  the  Use  of  Minerals  and  Statistics  of 

Domestic  Production 8vo.  1  00 

*  Pirsson's  Rocks  and  Rock  Minerals 12mo,  2  50 

*  Richards's  Synopsis  of  Mineral  Characters 12mo,  mor.  1   25 

*  Ries's  Clays:  Their  Occurrence,  Properties  and  Uses 8vo,  5  00 

*  Ries  and  Leighton's  History  of  the  Clay-working  Industry  of  the  United 

States 8vo,  2  50 

*  Tillman's  Text-book  of  Important  Minerals  and  Rocks 8vo.  2  00 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks 8vo,  2  00 


MINING. 

*  Beard's  Mine  Gases  and  Explosions .Large  12mo,  3  00 

Boyd's  Map  of  Southwest  Virginia Pocket-book  form,  2  00 

*  Crane's  Gold  and  Silver 8vo.  5  00 

*  Index  of  Mining  Engineering  Literature 8vo.  4  00 

*  8vo.  mor.  5  00 

Douglas's  Untechnical  Addresses  on  Technical  Subjects 12mo,  1  00 

Eissler's  Modern  High  Explosives 8vo.  4  00 

Goesel's  Minerals  and  Metals:  A  Reference  Book 16mo,  mor.  3  00 

Ihlseng's  Manual  of  Mining 8vo,  5  00 

*  Iles's  Lead  Smelting 12mo.  2  50 

Peele's  Compressed  Air  Plant  for  Mines 8vo.  3  00 

Riemer's  Shaft  Sinking  Under  Difficult  Conditions.     (Corning  and  Peele).8vo,  3  00 

*  Weaver's  Military  Explosives 8vo.  3  00 

Wilson's  Hydraulic  and  Placer  Mining.     2d  edition   rewritten 12mo,  2  50 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation 12mo,  1  25 

17 


SANITARY    SCIENCE. 

Association  of  State  and  National  Food  and  Dairy  Departments,  Hartford 

Meeting,  1906 8vo,  $3  00 

Jamestown  Meeting,  1907 8vo,  3  00 

*  Bashore's  Outlines  of  Practical  Sanitation 12mo,  1  25 

Sanitation  of  a  Country  House 12mo,  1  00 

Sanitation  of  Recreation  Camps  and  Parks 12mo,  1  00 

Folwell's  Sewerage.      (Designing,  Construction,  and  Maintenance.).  .'.  ..8vo,  3  00 

Water-supply  Engineering 8vo,  4  00 

Fowler's  Sewage  Works  Analyses 12mo,  2  00 

Fuertes's  Water-filtration  Works 12mo,  2  50 

Water  and  Public  Health 12mo,  1  50 

Gerhard's  Guide  to  Sanitary  Inspections 12mo,  1  50 

*  Modern  Baths  and  Bath  Houses 8vo,  3  00 

Sanitation  of  Public  Buildings 1 2mo,  1  50 

Hazen's  Clean  Water  and  How  to  Get  It Large  12mo,  1  50 

Filtration  of  Public  Water-supplies 8vo,  3  00 

Kinnicut,  Winslow  and  Pratt's  Purification  of  Sewage.      (In  Preparation.) 
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Control 8vo,  7  50 

Mason's  Examination  of  Water.     (Chemical  and  Bacteriological) 12mo,  1  25 

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*  Merriman's  Elements  of  Sanitary  Enigneering 8vo,  2  00 

Ogden's  Sewer  Construction 8vo,  3  00 

Sewer  Design 12mo,  2  00 

Parsons's  Disposal  of  Municipal  Refuse 8vo,  2  00 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
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*  Price's  Handbook  on  Sanitation 12mo,  1   50 

Richards's  Cost  of  Cleanness 12mo,  1  00 

Cost  of  Food.      A  Study  in  Dietaries 12mo,  1  00 

Cost  of  Living  as  Modified  by  Sanitary  Science 12mo,  1  00 

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*  Richards  and  Williams's  Dietary  Computer .8vo,  1  50 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Stand- 
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Mechanics'  Ready  Reference  Series) 16mo,  mor.  1  50 

Rideal's  Disinfection  and  the  Preservation  of  Food .8vo,  4  00 

Sewage  and  Bacterial  Purification  of  Sewage 8vo,  4  00 

Soper's  Air  and  Ventilation  of  Subways 12mo,  2  50 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  00 

Venable's  Garbage  Crematories  in  America 8vo,  2  00 

Method  and  Devices  for  Bacterial  Treatment  of  Sewage 8vo,  3  00 

Ward  and  Whipple's  Freshwater  Biology.      (In  Press.) 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

*  Typhoid  Fever Large  12mo.  3  00 

Value  of  Pure  Water L^-ge  12mo,  1  00 

Winslow's  Systematic  Relationship  of  the  Coccacea? Large  12mo,  2  50 


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Emmons's  Geological  Guide-book  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  8vo.  1  50 

Ferrel's  Popular  Treatise  on  the  Winds 8vo,  4  00 

Fitzgerald's  Boston  Machinist , .  18mo,  1  00 

Gannett's  Statistical  Abstract  of  the  World 24mo,  75 

Haines's  American  Railway  Management 12mo,  2  50 

Hanausek's  The  Microscopy  of  Technical  Products.     (Winton) 8vo,  5  00 

18 


Jacobs's  Betterment    Briefs.      A    Collection    of    Published    Papers    on    Or-  . 

ganized  Industrial  Efficiency 8vo,  $3  50 

Metcalfe's  Cost  of  Manufactures,  and  the  Administration  of  Workshops.. 8 vo,  5  00 

Putnam's  Nautical  Charts 8vo,  2  OO 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute  1824-1894. 

Large  12mo,  3  OO 

Rotherham's  Emphasised  New  Testament Large  8vo,  2  00 

Rust's  Ex-Meridian  Altitude,  Azimuth  and  Star-finding  Tables 8vo,  5  00 

Standage's  Decoration  of  Wood,  Glass,  Metal,  etc 12mo,  2  00 

Thome's  Structural  and  Physiological  Botany.      (Bennett) 16mo,  2  25 

Westermaier's  Compendium  of  General  Botany.      (Schneider) 8vo,  2  00 

Winslow's  Elements  of  Applied  Microscopy 12mo,  1  50 


HEBREW   AND    CHALDEE    TEXT-BOOOKS. 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

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UNIVERSITY 

OF 


NAM*:, 

Class  Course  Party. 


FIELD  NOTE-BOOH 


Note:      This   FIELD   NOTE-BOOK 'is  for  use  with  the  book  EXERCISI 

YINC  by  John  Clayton  Tracy,  C.  E.     It  may  be  inserted  in  the  back  of th 

md  held  in  place  by  tjie  elastic  band  provided  for  that  purpose.     Open  the  note-bo 

enter,  and  s.1  p  one  half  under  the  band  so*  as  to  bring  the  elastic  down  through  t 

center  of  the  note-book. 

It  is  suggested  that  each  student  keep  two  note-books  to  be  used  alternately.     Th 
one  may  beJianded  in  for  inspeciion  at  the  close  of  a  day's  work  and  the  other  used 
the  following  day  or' until  the  first  is  returned.     Additional  note-books  may  be  obtain 
ach  of  the  publishers,  John  Wiley  and  Sons  of  New  York  City. 

SUGGESTIONS 

C I )     Reserve  the  first  few  pages  for  an  index  of  exercises. 
(2)    At  the  top  of  each  page  print  a  descriptive  title. 

Number  the  exercises  to  correspond  to  the  numbering  in  the  book  of  exercise 
ample,  L-6  or  T-4. 

Date  each  exercise,  and  give  the  names,  of  other  members  of  the  party. 
Do  not  seribbltt  in  the  note-book.     Pay  particular  attention  to  neatne 
^snt.   . 

For  additional  suggestions  qn  keeping  field  notes  read  Chapter  III  on   /•'«> 
a  the  author's  text-book  PLANE  SURVEYING. 


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